
Class 7 qCsOO 
Book k_2 

copjgtitN°_ ^y^ 



COPYRIGHT DEPOSIT. 



THE 

TINSMITH'S HELPER 



AND 



PATTERN BOOK 



WITH USEFUL RULES, DIAGRAMS AND 
TABLES 



BY H. K. VOSBURGH 

Revised by 
WILLIAM NEUBECKER 



SE I 'EX TH EDI TION 



NEW YORK 
DAVID WILLIAMS COMPANY 

239 West 39th Street 

1912 



r 



Copyright, 1906 
BY DAVID WILLIAMS CO. 



Copyright, 1912 
BY DAVID WILLIAMS CO. 



y\ . 



■ 6 
£CIA312022 



INTRODUCTORY. 

The aim in preparing this little manual has been to 
make it a guide for the apprentice, journeyman and 
master sheet metal worker. To this end the author col- 
lected everything of value on the subject and then boiled 
it down to a well arranged series of simple problems on 
the different phases of pattern drafting which the 
mechanic has to puzzle over daily. 

The section on Mensuration will be found both accu- 
rate and complete and the rules and examples are reduced 
to the plainest language so that any one may understand 
them. Realizing the value of reliable data, he included 
all the tables of weights of materials, measures of area, 
capacity, etc., to which the sheet metal worker has occa- 
sion to refer, together with many excellent recipes, 
formulas and rules, which will be found of great service. 

The present edition has been carefully edited and 
revised by William Neubecker, expert pattern cutter and 
instructor at the New York Trade School. While the 
greater portion of the work remains intact, quite a num- 
ber of important changes have been made, to insure 
greater accuracy, and many simpler methods have been 
included. 

The Publishers. 

December 6, 191 1. 



INDEX 



PAGE 

Aluminum and copper sheets, relative weight 96-97 

Aluminum solder 120 

Apothecaries' weight table 109 

Arc, to find the center of 7 

Areas and circumferences of circles 98-104 

Arithmetical signs, definitions 74 

Avoirdupois weight, table 109 

Balls, to. describe gores for pattern 32 

Black sheet iron, standard gauges 89 

Boiler block, description of 66 

Boiler, oval, to find length of sheet required 26 

Breasts for cans, to describe 10 

Can breasts, pattern for 1 1-12 

Cans one inch deep, capacity of 106 

Capacities of bodies, mensuration of 85 

Cement for apparatus, corks, &c 1 19 

Cement for bottle corks 115 

Cement for china 116 

Cement for coppersmiths and engineers 115 

Cement for cracks in wood 118 

Cement for fastening blades, files, &c 119 

Cement for fastening brass to glass vessels 119 

Cement for holes in castings 115 

Cement, iron rust 114 

v 



VI 



Index 



PAGE 

Cement for iron tubes, boilers, &c 114 

Cement for ivory, mother of pearl, &c 114 

Cement for joining metals and wood 118 

Cement for leather 116 

Cement for marble workers and coppersmiths 116 

Cement for mending earthen and glass ware 1 14 

Cement for repairing fractured bodies of all kinds.. . 118 

Cement for stone ware 114 

Cement, gas fitters' 118 

Cement, hydraulic cement paint 119 

Cement, marble 116 

Cement, plumbers' 115 

Cement to mend iron pots and pans 117 

Cement to render cisterns and casks water tight. ... 117 

Cement to stop a leaky roof 119 

Cement, transparent for glass 117 

Center of an arc, to find the 7 

Circle, to describe octagon within 9 

Circles, mensuration of 79-83 

Circles, tables of circumferences and areas 98-104 

Circumferences and areas of circles 98-104 

Cisterns and tanks, number of barrels in.. . . 107, 108, 109 

Coffee pots, tables of sizes ill 

Cone, old German rule for patterns 18 

Cone, pattern for 13 

Cones and pyramids, to find the convex surface of . . 84 

Cones and pyramids, to find the solidity of 86 

Cones, mensuration of 73 

Copper sheets, weight 9°~97 

Cover, oval boiler, pattern for 2y 



Index vii 

PAGE 

Cubes, mensuration of 72 

Cylinders, mensuration of 7°~7 l 

Cylinders, to find the convex surface of 83-84 

Cylinders, to find the solidity of 86 

Cylindrical measures 105 

Cylindrical vessels, to find the contents in gallons of. 86 
Decimal equivalents to fractional parts of lineal 

measurement 75 

Definitions of arithmetical signs 74 

Dippers, tables of sizes in 

Dish kettles and pails, tables of sizes in 

Druggists' and liquor dealers' measures, tables of 

sizes in 

Dry measure, table no 

Elbow in five sections, pattern for 58 

Elbow, obtuse, to describe pattern for 60 

Elbow, tapering, to describe 61 

Elbow, to describe, quick method 53 

Elbow, three piece, to describe 54 

Ellipse or oval, to find the area of an 83 

Ellipse or oval, to find the circumference of an 83 

Ellipses, mensuration of 73 

Flaring article, square top, rectangle base, to describe 

pattern 46 

Flaring article, top and base rectangles, pattern for. . 48 
Flaring article, with straight sides and round ends, to 

describe patterns 42 

Flaring hexagon article, to describe pattern 44 

Flaring oval vessel, two pieces, to describe pattern. . 40 

Flaring square vessel, to describe pattern 45 



viii Index 

PAGE 

Flaring tinware, to describe patterns for 16 

Flaring vessel in three pieces 20 

Flaring vessels, to describe pattern for 14 

Flux for soldering tin roof 119 

Four-piece elbow, to describe 56 

Frustum of a cone, pattern 19-21 

Frustum of a cone, to find the contents in U. S. 

standard gallons 87 

Frustum of a cone, to find the solidity of 87 

Frustum of a pyramid, to find the solidity of the. . .87-88 

Frustums of cones, mensuration of j$ 

Funnel, rectangular, pattern for 22 

Galvanized sheets dimensions 91 

Galvanized sheets, weight 91 

Gores for balls, to describe pattern for 32 

Heart with square and compass 30 

Hexagon article, flaring, to describe pattern 44 

Hood for stove pipes, to cut 15 

Iron, black sheet, standard gauges 89 

Iron plate, weight of 89 

Lead pipe, weight per foot 92 

Lead, sheet, weight of 90 

Lineal measurement, decimal equivalents to frac- 
tional parts of 75 

Liquid measure, table no 

Measure, lip, pattern 28 

Measures of capacity, dry no 

Measures of capacity, liquid no 

Measures of weight, Avoirdupois 109 

Measures, tables of sizes in 



Index ix 

TAGE 

Mensuration, epitome of. 69 

Mensuration of the circle, cylinder, sphere, &c 69-71 

Mensuration of ellipses, cones, frustums, &c J$ 

Mensuration of solids and capacities of bodies 85 

Mensuration of the square, rectangle, cube, &c 71-72 

Mensuration of surfaces 76 

Mensuration of triangles, polygons, &c 72 

Metric system, and U. S. measures compared 110 

Obtuse elbow, to describe pattern for 60 

Octagon, tapering, to describe 47 

Octagon, within circle, to describe 9 

Octagon, within square, to describe 8 

Oval boiler cover 27 

Oval boiler, to find length of sheet 26 

Oval flaring vessel, four pieces, to describe patterns. 43 

Oval, to describe 34 - 3°\ 37 

Oval, to describe by string, pins and pencil 38 

Oval with diameters as 5 to 8, to describe 35 

Pans, table of sizes in 

Pipes of various metals, weights 91 

Pitched cover, pattern for 29 

Plate iron, weight 89 

Polygons, mensuration of 72 

Polygons, to find the area of regular 78 

Rectangle, mensuration of a 7 l ~7 2 

Rectangular base and round top article, pattern for. . 50 

Rectangular funnel, pattern 22 

Right angle elbow, to describe 52 

Round base and square top article, pattern for 49 

Round top and rectangular base article, pattern for. . 50 



X 



Index 



PAGE 

Round top and square base article, pattern for 51 

Rules for calculating circumferences 107 

Scale tray or scoop, pattern for 24 

Scoop or scale tray, pattern for 24 

Sheet lead, weight . 90 

Sheet zinc, weight per sheet 95 

Solder, aluminum 120 

Solder, black 113 

Solder for copper 113 

Solder for steel joints 113 

Solder, hard 113 

Solder, pewterers' 113 

Solder, plumbers' 113 

Solder, silver 112 

Solder, silver, for plated metal 113 

Solder, soft gold 113 

Solder, tinners' 113 

Solder, white for raised Britannia ware 112 

Solder, white for silver 112 

Solder, yellow for brass or copper 112-113 

Soldering fluid or flux 120 

Solids, mensuration of 85 

Sphere, mensuration of the J^l 1 

Sphere, to find the solidity of a 88 

Spheres, to find the convex surface of 85 

Square base and round top article, pattern for 51 

Square, mensuration of a 71 

Square, to describe octagon within 8 

Square top and round base article, pattern for 49 

Square vessel, flaring, to describe pattern 45 



Index 



XI 



PAGE 

Star, pattern for 31 

Steamer or pitched cover, pattern 29 

Strainer pail or watering pot breast, pattern 23 

Stringing patterns, mode of 64 

String pattern 65 

Surface, mensuration of 76 

Table, capacity of any cylindrical measure 105 

Table, effects upon bodies by heat 112 

Tables, circumferences and areas of circles 98-104 

Tables, rules and recipes (See special subject) 89 

Tapering elbow, to describe 61 

Tapering octagon, to describe 47 

Tea kettle body, to obtain length of piece 63 

Three-piece elbow, to describe a 54 

Tin plates, net weight per box 93~94 

Triangles, mensuration of y2 

Triangles, to find the areas yy 

Wash bowls, table of sizes in 

Water pressure per square inch 109 

Water, weight of 107 

Watering pot breasts, pattern for 23 

Weights of materials (See various materials). 

Weights of various substances no 

Zinc, sheet weight of 95 



DIAGRAMS AND PATTERNS. 



To Find the Center of an Arc. 



Fig. i. 




Let H K represent the given arc. Span dividers any 
convenient radius and describe small arcs, as V O. Draw 
lines through them, as shown by dotted lines, and the in- 
tersection, S, will be center sought, 



Rules and Diagrams. 



To Describe an Octagon Within a Given Square, 



Fig. 2. 




Draw diagonal lines from corner to corner and the in- 
tersection is the center H. With the compasses set to a 
radius from center to corner, and one foot set successively 
at each corner, describe the arcs, as shown. The points at 
which they cut the square, as K V, will be the corners of 
the octagon. Draw lines from point to point to complete 
the figure. 



Rules and Diagrams. 



To Describe an Octagon Within a Given Circle. 



Fit- 3- 













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v j 


V\k 


Ja 


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v/7 


\ \ \ 




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/ 1 1 


V / 










\_ V 


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Draw lines at right angles passing through the center 
H. This divides the circle into four equal parts, which 
need only to be subdivided into equal parts again 'to form 
the corners for the octagon. This may be easily done by 
drawing the lines K V, bisecting, as shown, and drawing 
lines to the circle. 

The bottom will correspond in size to the size of the 
circle or square. Remember to allow for burr and double 
seam. 



io 



Rules and Diagrams. 



To Describe Breasts for Cans. 



Fig. 4. 




Draw horizontal line II K, another parallel to it, V O, 
making- the distance between the desired hight of breast. 
On H K lay off diameter of can, as S B. On V O, size of 
opening as U R, produce lines B R, S U, until they cross 
G. Span dividers from G to S, describe outer circle. G 
to U, describe inner circle. Set off outer circle equal to 
the diameter of the can B S. Starting at B, draw line 
from G, allowing for locks, as shown by dotted lines. 
Reference can be made to the circumference table. 



Rules and Diagrams. 

Can Breasts. 

Fig- 5- 



11 




Draw the two horizontal lines, K V and O S, and per- 
pendicular to them the line K H. Set off on line K V 
from the point K one-half the diameter of the can. On O 
S the point R is one-half the diameter of the opening. 
Produce the line U G, touching the points B and R, until 
it intersects H K. From U as center, with the radius U 
B, describe the outer circle. With the radius U R, the 
inner. Then span from K to B and step six times on large 
circle to obtain size of breast. Draw line to center and al- 
low for locks, as shown by dotted lines. 



12 



Rules and Diagrams. 



Can Breasts. 

Fig. 6. 




Describe circle size of can. Draw line through center 
H. Span dividers three-fourths of diameter and strike 
circle K V. Span to diameter of can and step three times 
on large circle. 

Draw line from center to points K V, allowing for 
edges and locks. For more or less pitch make circle K 
V larger or smaller. 

Small circle in center for opening in top. Hoods and 
pitched covers may be cut by same rule. 



Rules and Diagrams. 



13 



Pattern for Cone. 



Fig- 7. 




H K V represents a cone for which an envelope is 
wanted. 

Span the dividers from V to H and describe the arc 
O S. Set off the arc equal in length to the circumference 
of the required cone. Draw the lines V O and V S, allow- 
ing for locks or laps, as shown by the dotted lines. 

For the circumference, refer to the tables or obtain by 
some of the rules. By using the rules familiarity with 
them is obtained, which is desirable. 



M 



Rules and Diagrams. 



To Describe Pattern for Flaring Vessels. 



Fig. 8. 




For example, it is desired to describe pattern for pail 
12 inches in diameter at top, 9 inches at bottom and 9 
deep. 

Take the difference between large and small diameters 
(3 inches) for the first term, the hight for the second and 
the large diameter for the third, thus, 3 : 9 : : 12. 

12x9^-3, this gives radius by which the pattern may- 
be described. Span the dividers (or use beam compasses, 
piece of wire, straight edge or any convenient device) 36 
inches and strike large circle. With radius less the 
slant hight of pail strike small circle. Ascertain the cir- 



Rules and Diagrams. 15 

cumference required and divide by the number of pieces 
to be used. Lay off on outer circle and draw lines to cen- 
ter, as H K V. 

Allow for locks, burr and wire. 



To Cut Hood for Stove Pipes. 

Span dividers size of pipe, describe circle, cut in to 
center, lap over and rivet. 



Rules and Diagrams. 



To Describe Patterns for Flaring Tinware. 



Fig. o. 




By this figure and rule can be drawn any article of flar- 
ing tinware of any diameter, large or small. It is a rule 
of more extensive application than any other for getting 
correct patterns for frustums of a cone. It is the foun- 
dation for all curved work, cornice, bevels, chamfers, etc. 

H K V O represents the elevation of an ordinary tin 
pan, constructed in four pieces, 15J/2 inches in diameter at 
the top. Below the elevation is shown the same in plan ; 
the pan is a frustum of a cone, and if the sides of the pan 



Rules and Diagrams. iy 

were continued down until they intersected at S, as shown, 
the cone would be complete. The radius of the envelope 
of the cone must be either S H or S K. To describe the 
section of the frustum which is required, place one foot 
of the dividers at the center S, and with the radius S H de- 
scribe the arc K B. With the radius S V describe O U. 
This gives the width of pattern and the proper sweep. 

To get the length of the piece, refer to the table of 
circumferences or find, by the rules given, the circumfer- 
ence of the article, which in this case is 48^6 inches. There 
being four pieces, divide by four, which gives 12 5-32 
inches; span the dividers 1 inch, step off the 12 and add 
the fraction. 

Draw line from center S to point last ascertained. For 
locks, wire edge and burr allowance must be made. 



18 



Rules and Diagrams. 



The Old German Rule for Patterns for the Cone. 



Fig. io. 




Take the slant hight of the cone H K as a radius, and 
describe a circle. Divide the diameter of the base of the 
cone K V into seven equal parts and set off a space equal to 
twenty-two of these parts on the circle already struck. 
From the extremities thus measured off draw lines to the 
center. 

Allow for locks. 



Rules and Diagrams. 

Frustum of a Cone. 

Fig. ii. 



19 




Lay the square on your sheet and construct the right 
angle H K V. Draw line O S parallel to K V, making the 
distance K O the altitude. On these lines lay off one-half 
the diameter of the large and small ends. Draw line 
through points V and S until they intersect at H ; then, 
with H as the center, describe the semicircles B U, R G. 
Lay off circumference of large end on line B U and draw 
lines to center H. Must allow for all edges. For two 
sections take one-half of the piece, allowing edges on 
piece used for pattern. 



20 



Rules and Diagrams. 



Flaring Vessel in Three Pieces. 



Fig. 12. 




Draw line H K ; perpendicular to it, lines parallel to 
each other apart the hight of vessel. With the intersec- 
tions, as V, O for centers, describe circles size of top and 
bottom of vessel. Draw lines S H and B H touching on 
circles, and at intersection H as center, with the radius H 
V, describe the segment U R ; with the radius H O, the 
segment G F. Allow for locks, as shown by dotted lines. 



Rules and Diagrams. 



21 



Frustum of a Cone 



Fig- J 3- 




Draw perpendicular line H K, and from K lay off 
diameter of large end, as V O ; on the line H K the hight 
of frustum, as K S. Draw line parallel to V O, and on it 
lay off small diameter, as B U. Draw lines through points 
V B and O U until they intersect at H. Span compasses 
from H to V and draw large arc R G ; from H to B and 
describe small arc ; make arc R G equal to circumference 
of large diameter and draw lines to center H. Allow for 
all edges, wire, burr and locks. This forms a pattern in 
one piece. 



22 



Rules and Diagrams. 

Rectangular Funnel. 

Fig. 14. 



K 




Draw side, as H K V. Continue side lines, as shown 
by dots. From point of intersection as center, describe 
arc and chord K V and H. Draw end O K S, producing 
lines to intersect at B. From B as center describe arc and 
chord O K and S. The other side and end obtained in the 
same manner, as shown in cut. Can be made in two or 
more pieces by dividing. All locks and edges must be 
allowed for on the pattern piece. 



Rules and Diagrams. 



aj 



For Strainer Pail or Watering Pot Breast. 



Fig- *5- 




Strike circle size of pail or pot. Span dividers ij4 
inches, more or less, than radius of circle, being governed 
by pitch desired, as from V to K, and describe the arc. 
Draw the chord, making the segment K O which is the 
pattern of the desired width. The breast may be cut out if 
preferred, as shown by dotted lines. 



24 



Rules and Diagrams. 



Scale Tray or Scoop. 



Fig. 16. 




Construct a sectional view of the scoops, as H K V; 
it being made in two pieces as O, let H S B represent 
one-half elevation of it. Continue the lines B S and K H 
until they cross at U. Divide H K V into any given 
number of spaces, continuing the same to the line H B, 
as shown by short lines. Draw lines from the division 



Rules and Diagrams. 25 

points on H B to the joint U, thus obtaining the inter- 
sections on the line S H. With the T square at right 
angles with H U, drop the points thus obtained on H S, 
onto the line B S. 

With U as center and U B as a radius describe the 
arc B R. Step off upon this arc spaces equal to those in 
H K V, using dividers, which gives the length B R. 
Draw radial lines from U to space marks on line B R, as 
shown. 

With U as center and the various points on S B as 
radii, describe arcs, intersecting similar radial lines as 
shown. Then a line traced through the points thus 
obtained, together with the arc B R, will be the outline 
of the required pattern. Allow for edges, as shown by 
dotted lines. 



26 



Rules and Diagrams. 



To Find Length of Sheet Required for Oval Boiler. 
Common Method. 

Fig. 17. 




Describe bottom, length and width desired, then burr 
and from H as a starting point roll on the bench to obtain 
circumference. If three piece- are to be used, divide the 
circumference into three parts and allow edges; if made 
in two pieces, divide by two. Always divide the circum- 
ference by the number of pieces desired. Cut the cover 
the same size as bottom. 



Rules and Diagrams. 



27 



Oval Boiler Cover. 



Fig. 18. 




Draw line A K, and from R as center describe circle 
G U, size of boiler outside of rod. Make A K equal to 
one-half of entire length of boiler, and KS ^ inch or 
more if more pitch is desired. Through S draw the per- 
pendicular line H V. Lay corner of square on line H, 
one blade at K, the other touching circle, describe lines 
U H K; in similar manner obtain K V G. Allow for 
locks and notch for edges. 



28 



Rules and Diagrams. 



Measure Lip. 



Fig. /o. 




Draw line H K and upon it, with V as center, describe 
circle size of measure. With S as center, being the half 
distance from V to H, describe semicircle B. U. Make 
R K the desired width. With V as center describe G O. 
Cut on B U and G O to obtain the lip. 



Rules and Diagrams. 



29 



Steamer or Pitched Cover. 
Fig. 20. 




Strike circle 1 inch larger than rim burred. Draw 
line through center H, and from either side cut 1 inch on 
circle to 1 inch from center K. Draw lines and cut out. 
Or, strike circle the same or larger. Draw line through 
center and cut on it to center. After burring put in rim; 
draw up and mark, cut out triangular piece and solder, 
Much quicker and equally as good. 



30 



Rules and Diagrams. 



Heart with Square and Compass. 



Fig. 21. 




Draw line H K the breadth of the heart and on it two 
semicircles. Span dividers from H to K and make sweep 
toV. 



Rules and Diagrams. 



3* 



To Describe a Star. 

Fig. 22. 




From V as center strike circle size of star desired. 
Divide circle in five parts and draw lines to points. 

There is a rule for finding the points of a star other 
than stepping, but I do not give it. I have found the 
mode given to be the quickest and most accurate. 



32 



Rules and Diagrams. 



Pattern for Cutting Balls. — To Describe the Gores. 



Fig- *3- 




Erect perpendicular line H K equal to one-half the cir- 
cumference oi the ball; divide this line into one-half the 
number of pieces required in full ball ; make the line Y O 
equal to one of these pieces, cutting H K through the 
center at right angles; then with II and K as centers, with 
radius greater than one-half the distance K S, describe the 
two arcs B U; with V and O as centers, arcs R G; draw 



Rules and Diagrams. $$ 

lines through these points, as shown by dotted lines. 
From points of intersection describe arcs H V K and 
H O K, and you obtain pattern for one piece. Allow for 
laps or seams. The more pieces used the better globe 
produced. Good results obtained by slightly raising the 
pieces. 



34 



Rules and Diagrams. 



To Describe an Oval. 



Fig. 24. 




Draw horizontal line F K, span the dividers one-third 
the required major diameter, and from V and O as centers 
describe circles, as shown; then span dividers two-thirds 
entire length, and, with one foot at the intersection of the 
circles, as S and B, draw the arcs G H and U R, which 
completes the oval. 

The proportion of the diameters is about as 3 to 4. 



Rules and Diagrams, 



35 



To Describe Oval with Diameters as 5 to 8. 



Fig- 2 5- 




Draw horizontal line H K. Span compasses one- 
quarter the long diameter and describe three circles with 
that radius, as shown by diagram. Then draw lines 
through centers of outer circles and their intersections, 
as shown. The oval is completed by drawing the arcs con- 
necting the outer circles from points V and O as centers. 



3« 



Rules and Diagrams. 



To Describe an Oval. Another Method. 



Fig. 26. 




Draw horizontal line H K and perpendicular to it V O. 
Let H K equal the long or transverse diameter, and S B 
the short or conjugate. Lay off the distance S B on the 
line H K, as from H to U. Divide the distance U K into 
three equal parts. From R, the center, set off two of the 
parts each side, as G F. On the line Y O set off the dis- 
tance G F from R, as R Y and R O. From V and O 
draw lines passing through G and F, as shown. From 
the points V, O, G, F as centers describe the arcs that 
complete the ellipse. 



Rules and Diagrams. 

To Describe an Oval. Another Method. 

Fig. 27, 



37 




Construct the parallelogram equal in length and width 
to the long and short diameters of the oval desired. Di- 
vide it into four equal parts by drawing lines through the 
center, crossing at H. Mark the points K and K one-third 
the distance from V to H, and draw lines from the corners 
through these points until they intersect, as shown at O. 
Then from O and O as centers describe the arcs SUB 
and SUB; from K and K as centers the segments B V B 
and S V S. 



38 



Rules and Diagrams. 



To Describe Oval by Means of String, Pins and 

Pencil. 



Fig. 28. 




Erect perpendicular line H K equal to short diameter 
and at right angles to it V O. Span dividers one-half the 
length of the oval, and with H and K as centers describe 
the arcs S and B. Set pins at these points, and, with a 
string (one that will not stretch) tied around them so 
that the loop when drawn tight will reach H or K, as 
shown, draw the figure with pencil, keeping string equally 
tense while going around. Of all the apparatus invented 



Rules and Diagrams. 39 

for oval drawing I think the string is the best. The best 
results, at least, are obtained. To attempt to draw a per- 
fect oval or ellipse by the use of compasses is vain. It 
cannot be done so that the line will be true, or the propor- 
tion or shape satisfactory to one with an eye for correct- 
ness or uniformity. The so-called trammels are the next 
best thing, but no better. A few rules for drawing ovals 
by the use of dividers have been given in this work so 
the mechanic may take his choice, and after a little prac- 
tice with the string and nails will find them the best tram- 
mels yet invented for the purpose. 



4° 



Rules and Diagrams. 



To Describe Pattern for Flaring Oval Vessel. 
Two Pieces. 

Fig. 29. 




Draw plan according to rule given in Fig. 24, or any 
other method. Construct right angle triangle T H 1 S 1 
and parallel to H 1 S\ draw H 1 O 1 , the distance between 
hight of article. Lay off on H 1 S 1 the distances H S and 
V S in plan and on H 1 O 1 the distances H O and V O in 



Rules and Diagrams. 41 

plan. Draw lines through these points to intersect the 
line R 1 T at U and T. Using T as center draw the arcs 
O 1 K 1 and S 1 R\ making the distance along the arc S 1 R 1 
equal to U R in plan. Draw line from R 1 to T. Take 
radius V 1 U on the lines R 1 T and S 1 T and obtain centers 
B and C. with which describe the arcs R 1 G 1 and S 1 G\ 
which make equal in length to G R or U B in plan. Draw 
lines to centers B and C. Allow for all edges, locks, wire 
and burr. 



42 



Rules and Diagrams. 



To Describe Pattern for Flaring Article with Straight 
Sides and Round Ends. Two Pieces. 



Fig- 30. 





Erect two perpendicular lines, H V, K O, distance 
between the length of sides A B ; at right angles to these, 
two lines, distance between the slant highl of article C D. 
On II V and K O set off the radius C E as Y and O. 
From V and O as centers, with radii V B, V II and O S, 
< » K, draw the arcs B J, H G and S U, K R. Make the 
arcs H G and K R equal to one-half the circumference of 
the ends M N and draw lines to Y and O. Allow for all 
edges, locks, wire and burr. 



Rules and Diagrams. 

To Describe Pattern for Oval Flaring Vessel. 
Four Pieces. 

Fig- 3*- 



43 




Describe bottom as by Fig. 27. Obtain length of arcs 
SUB and S V S, also length of corresponding arcs at 
the top of vessel. Draw horizontal lines H K and V O, 
making the distance between the desired slant hight. 
Make H K equal in length to that of the piece at the top, 
and V O to that of the bottom, for the sides. S B and 
U R for the end pieces. Produce lines through these 
points to intersect at G and G\ Describe the arcs from 
these points. Allow for all edges, locks, wire and burr. 



44 Rules and Diagrams. 

To Describe Pattern for Flaring Hexagon Article. 

Fig. 32. 




Let V O represent width of the bottom of one side 
and R G the width of the top of one side, the distance 
between the slant hight. Produce side lines until they 
cross in the center, as shown by dotted lines. Span 
dividers from center to O, and describe circle H O U; 
span to G and describe inner circle ; span again from V 
to O and step on the outer circle three spaces each side 
from O, as K, H, B, S, U. Draw lines from these points 
tending toward center, and connect by chords as H K, 
K O, etc. Cut out piece H U, allowing for locks, as 
shown. Pattern for a pentagon article may be described 
bv the same rule. 



Rules and Diagrams. 



45 



To Describe Pattern for Flaring Square Vessel. 



Fig- 33- 




Let K Y and B U represent the width of the bottom 
and top of one of the sides, the distance between the slant 
hight. Continue lines until they intersect at R. With 
radius R B. strike circle U B G. Span dividers from K 
to V ana set orr on outer circle the distance, as V O, K S, 
etc. ; draw lines through these points tending toward the 
center R, also the chords, as shown by dotted lines. Allow 
for edges. Can be made in two pieces by dividing and 
allowing for extra lock or seam. 



46 



Rules and Diagrams. 



To Describe Pattern for Flaring Article with Square 
Top and Base a Rectangle. Two or Four Pieces. 

Fig- 34- 




Draw rectangular base H K and square top Y in 
center of base. Draw perpendiculars O S and R U. Also 
place the hight of the article O B and R G. Place the 
slant hight B S on B 1 S 1 and draw lines a and b which 
intersect as shown, which gives pattern for end. Place 
G U on G 1 U 1 , draw lines a' and b' which intersect as 
shown, which gives pattern for side. Join half of end 
pattern to either side of side pattern as shown by similar 
letters, which gives half pattern. 



Rules and Diagrams. 



47 



To Describe Tapering Octagon Article. 



Fig- 35- 




Draw bottom K II and top V of one side, with dis- 
tance between the slant hight, and continue side lines until 
they intersect at O. With O as a center and the radii 
O V and O H, describe inner and outer circles. Set off 
on them distances equal to H K and V, and connect by 
chords, as shown by dotted lines. Allow for locks and 
edges. 



4 8 



Rules and Diagrams. 



Flaring Article, Top and Base a Rectangle. Two 

Pieces. 



Fig- 3<5. 




Draw side elevation, as H K, V O, of the longest side. 
Span dividers the difference between the shortest side of 
the base and longest side of top. From Y and O as cen- 
ters describe arcs S and S. With blade of square resting 
on arcs and the corner at 1 1 and K, draw lines H B and 
K G. Set off H B and K G equal one-half of shortest 
sides of base and draw lines B U and G R at right angles 
to H B and K G ; also lines U V and R O at right angles 
to U B and G R. Allow for locks, as shown by dotted 
lines. For a strictly accurate pattern proceed as in Fig. 34. 



Rules and Diagrams. 



49 



Round Base and Square Top Article. Two Pieces. 



Fig. 37- 




Erect perpendicular lint. Span dividers to three- 
quarters diameter of base and describe semicircle H K V. 
Make K V and K H each equal to one-quarter the circum- 
ference of the round base and draw lines to center. Span 
dividers to three-quarters size of top from corner to cor- 
ner and describe inner circle. Lay out sides of top, size 
required, on circle, as shown. Allow laps. 



5° 



Rules and Diagrams. 



Rectangular Base and Round Top Article. 
Two Pieces. 

Fig- 38- 




Draw horizontal lines H K, V O. Make H K equal 
to the longest side of base, V O equal to one-fourth the 
circumference of the top, the distance between slant 
hight ; draw side lines through these points. With radii 
one-half the difference between V O and the shortest side 
of the base, describe the arcs S, B ; with blade of square 
resting on arcs, and corner at H and K, draw lines K R, 
H U, equal to one-half the short side ; at right angles to 
K R, H U, draw lines R G and U G ; U G and R G pro- 
duced will intersect ; from this point span dividers to line 
V O and describe the arc. Allow for locks and edges. 



Rules and Diagrams. 



5* 



Square Base and Round Top Article. Two Pieces. 



'Pig- 39- 




Draw horizontal lines H K, V O; H K equal to the 
length of one side of the base, V O equal to one-fourth 
the circumference of the top, the distance between the 
slant hight ; draw lines through these points. With radii 
one-half the difference between K H and O V, describe 
arcs ; with blade of square resting on arcs and the corner 
at H and K, draw lines H S and K B, equal to one-half 
the base ; at right angles to H S and K B draw S U and 
B R, produced to intersect at G. Span dividers from G to 
line V O and describe the arc. Allow for locks and edges. 



5 2 Rules and Diagrams. 

To Describe a Square or Right Angle Elbow. 
Two Pieces. 

Fig. 40. 




Draw the elevation of the elbow, as B S, O V, K H. 
Draw line from V to O. Divide one-half of the plan 
into a convenient number of equal parts, as shown by 
dotted lines ; erect lines to intersect O V. Make the line 
B R equal rn length to the circumference of the elbow. 
Set off on this line spaces corresponding to those in the 
plan, the same number each side of the center line ; then 
draw lines parallel to the arm of the elbow, cutting the 
corresponding lines as indicated. By tracing through 
these points the irregular line U G the pattern is obtained. 
Allow for locks or rivets. 

The general principle for cutting elbow patterns is the 
same throughout, and to understand the principle is to be 
able to describe pattern for any elbow, at any angle and 
of any number of pieces. It is the design of this work to 
make the principle clear. 



Rules and Diagrams. 



53 



Quick Method. 



Fig. 4i> 



K T 













U 








/f] 










V 

































B 

















Lay out on sheet length required for elbow, as H K 
V O. Describe semicircle S the desired size of pipe, 
which divide into four parts. Space the length of the 
sheet into twice the number of squares in S, and draw 
vertical and horizontal lines until they intersect. OBU 
R V is then an accurate pattern. Allow for flanges. 



54 



Rules and Diagrams. 



To Describe Three-Piece Elbow. 



Fig. 42. 




Let H K be the throat and K V the diameter of the 
elbow. Draw the quadrant Y O, which divide into four 
equal parts, as shown by i, 2, 3. Draw miter lines through 
1 and 3 as H R and H G. Draw the circle B equal to 
diameter of elbow and divide one-half of B in equal parts, 
as shown ; draw lines to intersect miter line R U. 



Rules and Diagrams* 



55 



Fig. 43- 















_R_ 
























R' 












9 


8 


7 


6 


5 


4 


8 


4 


5 


6 


7 


8 



Construct parallelogram H K V O equal in length to 
the circumference of B. Through the spaces on H K 
draw parallel lines as shown. Measuring from V K, take 
the various distances to the miter line R U and place them 
on similar lines measuring from H K. H S B K is then 
the pattern for the end. Double the distance from 3 to 
R 1 and place it from S to G and B to U and transfer the 
miter line S R 1 B to G R U. Place H S as shown by G O 
and U V and draw O V, which completes the three 
patterns. 



5* 



Rules and Diagrams. 



To Describe a Right Angle Elbow. Four Pieces. 



Fig. 44. 



v b 




Let H K be the throat and K V the diameter of the 
elbow. Draw the quarter circle V O, which divide into 
six equal parts, as shown by a b c d e. Draw miter line* 
through a, c and e, as shown by II B, H G and H F 
Draw the circle R, which space as shown, and draw lines 
to intersect the miter line B U. 



Rules and Diagrams. 



57 



Fig- 45- 




7 6 5 4 3 



4 5 t> 7 



Construct parallelogram H K V O, equal in length to 
the circle R, as shown by similar figures on H K, through 
which draw parallel lines as shown. Measuring from 
V K, take the various distances to the miter line B U and 
place them on similar lines in the pattern, measuring from 
H K, and obtain B S B. Double i S and place at B U 
and B U and trace the miter cut B S B as shown by 
U G U. Place S G at U T and U T and trace UGU 
as shown by T A T. Make T O and T V equal to S i 
and draw line O V, which completes the four patterns. 
Allow for locks. 



5» 



Rules and Diagrams. 



Elbow in Five Sections. 



Fig. 46. 




Draw throat H K and diameter K V. Draw quad- 
rant H Y R, which divide into eight parts as shown from 
a to g ; draw miter lines HU,HB,HS and H O. Divide 
profile A into equal spaces, and draw lines to miter line 
HO. 



Rules and Diagrams. 



59 



Fig- 47- 



F 














C 










— < 












u 

o 






G 
B 










H 




K 



3 4 5 6 7 



5 4 3 2 1 



Make I i equal to circumference of profile A. Draw 
parallel lines as shown in pattern. Use dividers and meas- 
ure various distances from V K to miter line H O, which 
transfer to similar lines measuring from i i, and obtain 
miter cut H K V. Double 7 K and place at H O and V S 
and draw miter cut O B S. Place KBatOU and S R 
and draw miter cut U G R. Make U A and R D equal 
to H O and draw miter cut A C D. Make A F and D E 
equal to H i and draw F E, which completes the five pat- 
terns. Allow for locks. 



6o Rules and Diagrams. 

To Describe Pattern for Obtuse Elbow. 



Fig. 48. 




When the pattern for an obtuse elbow is desired it it 
only necessary to draw a correct representation of the 
elbow and obtain the miter line, as follows : With H as 
center, draw the arc K V. With any desired radius, and 
using K and V as centers, intersect arcs at O. Draw the 
miter line H O S. Place the half profile B in position as 
shown, which space, and draw parallel lines to the miter 
line H S. Then proceed as by the rules already given, and 
the result will be satisfactory. 



Rules and Diagrams. 



61 



To Describe a Tapering Elbow 



Fig. 49. 




62 Rules and Diagrams. 



Draw elevation of elbow at any angle desired and 
draw miter line H K as shown. Establish hight and diam- 
eter of small end as Y O and extend the lines i-V and 
7-O until they meet at B. Draw half profile S, which 
space into equal parts and draw vertical lines to 1-7, from 
which draw radial lines to the apex B, which will cross 
the miter line H K as shown. From these intersections 
draw horizontal lines to the side B-7 as shown from 1 
to 7. With B-7 as radius, draw the arc y'-f equal to the 
circumference of the circle S. From the points on j'-J 
draw radial lines to the apex B, which intersect by arcs 
struck from B as center, with radii equal to the points 
between 1 and 7. U R G O is the pattern for the upper 
arm and R G y'-y' pattern for the lower arm. Allow for 
locks. 



Rules and Diagrams. 



«3 



To Obtain Length of Piece for Tea Kettle Body 



Fig. 50. 




\ ,—. (' 
-J 



u 



'7 



The way in general practice is to roll the bottom after 
burring on the bench to obtain circumference, and use 
strip 24 i ncn l ess m length, as shown by figure. H repre- 
sents the pit ; K V the length of the strip or sheet. 



$4 



Rules and Diagrams. 



Mode of Stringing Patterns. 



Fig- 51- 




This cut represents the three pieces of a 6-quart pan 
usually cut from one sheet of 10 x 14 tin. Instead of using 
one piece for pattern and placing it three times, three 
pieces are fastened together by soldering on two strips of 
tin with a heavy hem on each side, and all placed at once, 
thus saving time and vexation. To use to advantage 
begin at the bottom of the string pattern and mark around 
on the outside first, and then mark in the centers. 



Rules and Diagrams. 



65 



String Pattern. 

Fig. 5 2 - 



H2 



This figure represents a string of rim or hoop pat- 
terns, fastened as shown in the same manner as described 
on page 64. Rims of any width can be put together in 
this manner and a great saving of time is the result when 
once properly done. Patterns for all articles of tinware 
should be strung in this way, when more than one piece 
is obtained from a sheet, that the marking out may be ex- 
pedited and less tedious. 



66 



Rules and Diagrams. 



Description of Boiler Block. 



Fig- 53- 



Tiy this figure is represented a block for truing - up 
boilers after they are formed up in the rollers and locked 
together. Many mechanics depend upon the stake and 
the accuracy of the eye, but after using this method would 
not abandon it, as better results are obtained and in much 
less time. The block is made of 2-inch [lank, by placing 
one on another and securing with four long bolts passing 
through them. The proper dimensions are as follows : 

Bottom, 13 inches wide, 25 inches long. 

Top, 10 " " 19 " 

Hight, 12 " 



APPENDIX. 



EPITOME OF MENSURATION. 



OP THE CIRCLE, CYLINDER, SPHERE, ETC. 

i. The circle contains a greater area than any other 
plane figure bounded by an equal perimeter or outline. 

2. The areas of circles are to each other as the squares 
of their diameters. 

3. The diameter of a circle being 1, its circumference 
equals 3.1416. 

4. The diameter of a circle is equal to .31831 of its 
circumference. 

5. The square of the diameter of a circle being 1, its 
area equals .7854. 

6. The square root of the area of a circle multiplied 
by 1. 1 2837 equals its diameter. 

7. The diameter of a circle multiplied by .8862, or the 
circumference multiplied by .2821, equals the side of a 
square of equal area. 

8. The number of degrees contained in the arc of a 
circle multiplied by the diameter of the circle and by 
.008727, the product equals the length of the arc in equal 
terms of unity. 

9. The length of the arc of a sector of a circle multi- 
plied by its radius equals twice the area of the sector. 

10. The area of the segment of a circle equals the area 
of the sector, minus the area of a triangle whose vertex 



70 Epitome of Mensuration. 

is the center and whose base equals the chord of the seg- 
ment. 

1 1. The sum of the diameters of two concentric circles 
multiplied by their difference and by .7854 equals the area 
of the ring or space contained between them. 

12. The circumference of a cylinder multiplied by its 
length or hight equals its convex surface. 

13. The area of the end of a clyinder multiplied by its 
length equals its solid contents. 

14. The area of the internal diameter of a cylinder 
multiplied by its depth equals its cubical capacity. 

15. The square of the diameter of a cylinder multiplied 
by its length and divided by any other required length, 
the square root of the quotient equals the diameter of the 
other cylinder of equal contents or capacity. 

16. The square of the diameter of a sphere multiplied 
by 3.1416 equals its convex surface. 

17. The cube of the diameter of a sphere multiplied 
by .5236 equals its solid contents. 

18. The hight of any spherical segment or zone, multi- 
plied by the diameter of the sphere of which it is a part 
and by 3.1416, equals the area or convex surface of the 
segment ; or, 

19. The hight of the segment multiplied by the cir- 
cumference of the sphere of which it is a part equals the 
area. 

20. The solidity of any spherical segment is equal to 
three times the square of the radius of its base, plus the 
square of its hight. multiplied by its hight and by .5236. 

21. The solidity of a spherical zone equals the sum 
of the squares of the radii of its two ends and one-third 



Epitome of Mensuration. 71 

the square of its bight, multiplied by the hight and by 
1.5708. 

22. The capacity of a cylinder, 1 foot in diameter and 
1 foot in length, equals 5.875 United States gallons. 

23. The capacity of a cylinder, 1 inch in diameter and 
1 foot in length, equals .0408 United States gallon. 

24. The capacity of a cylinder, 1 inch in diameter and 
1 inch in length, equals .0034 United States gallon. 

25. The capacity of a sphere 1 foot in diameter equals 
3.9168 United States gallons. 

26. The capacity of a sphere 1 inch in diameter equals 
.002266 United States gallon ; hence, 

2J. The capacity of any other cylinder in United States 
gallons is obtained by multiplying the square of its diame- 
ter by its length, or the capacity of any other sphere by the 
cube of its diameter and by the number of United States 
gallons contained as above in the unity of its measurement. 

OF THE SQUARE, RECTANGLE, CUBE, ETC. 

1. The side of a square equals the square root of its 
area. 

2. The area of a square equals the square of one of its 
sides. 

3. The diagonal of a square equals the square root of 
twice the square of its side. 

4. The side of a square is equal to the square root of 
half the square of its diagonal. 

5. The side of a square equal to the diagonal of a given 
square contains double the area of the given square. 

6. The area of a rectangle equals its length multiplied 
bv its breadth, 



72 Epitome of Mensuration. 

7. The length of a recangle equals the area divided by 
the breadth ; or the breadth equals the area divided by the 
length. 

8. The solidity of a cube equals the area of one of its 
sides multiplied by the length or breadth of one of its 
sides. 

9. The length of a side of a cube equals the cube root 
of its solidity. 

10. The capacity of a 12-inch tube equals 7.48 United 
States gallons. 

OF TRIANGLES, POLYGONS, ETC. 

1. The complement of an angle is its defect from a 
right angle. 

2. The supplement of an angle is its defect from two 
right angles. 

3. The three angles of every triangle are equal to two 
right angles : hence the oblique angles of a right angled 
triangle are each other's complements. 

4. The sum of the squares of two given sides of a 
right angled triangle is equal to the square of the hypothe- 
nuse. 

5. The difference between the squares of the hypothe- 
nuse and given side of a right angled triangle is equal to 
the square of the required side. 

6. The area of a triangle equals half the product of the 
base multiplied by the perpendicular hight. 

7. The side of any regular polygon multiplied by its 
apothem or perpendicular, and by the number of its sides, 
equals twice the area. 



Epitome of Mensuration. 73 

OF ELLIPSES, CONES, FRUSTUMS, ETC. 

1. The square root of half the sum of the squares of 
the two diameters of an ellipse multiplied by 3.1416 equals 
its circumference. 

2. The product of the two axes of an ellipse multiplied 
by .7854 equals its area. 

3. The curve surface of a cone is equal to half the 
product of the circumference of its base multiplied by its 
slant side, to which, if the area of the base be added, the 
sum is the whole surface. 

4. The solidity of a cone equals one-third the product 
of its base multiplied by its altitude or hight. 

5. The square of the diameters of the two ends of the 
frustum of a cone added to the product of the two diame- 
ters, and that sum multiplied by its hight and by .2618, 
equals its solidity. 



DEFINITIONS OF ARITHMETICAL SIGNS USED 
IN THE FOLLOWING CALCULATIONS. 



= Sign of Equality, and signifies as 4 + 6 = 10. 



Addition, " 

Subtraction, " 

Multiplication, " 

Division, ' k 

Square Root, " 

to be squared, " 

to be cubed, " 



as 6 + 6 = 12, the Sum 

as 6 — 2=4, Remain- 
der. 

as 8 x 3 = 24, Product. 

as 24 + 3 = 8, 

Extraction of Square 
Root. 

thus 8 2 = 64. 

thus 3 3 = 27. 



DECIMAL EQUIVALENTS TO FRACTIONAL 
PARTS OF LINEAL MEASUREMENT. 



.8333 
.75 

.0666 



.4166 
.3333 
.25 



ONE INCH THE INTEGER OR WHOLE NUMBER. 



,96875 equal T s and 3-32 


.46875 


equal 


% and 3-32 


9375 


T . and 1-16 


.4375 


" 


%and 1-16 


,90625 


% and 1-32 


.4iT.LT, 


" 


% and 1-32 


S75 


% 


.37r, 


" 


% 


,84375 


% and 3-32 


.34375 


" 


V 4 and 3-32 


8125 


% and 1-16 


.3125 


" 


*A and 1-16 


78125 


% and 1-32 


.28125 


" 


y 4 and 1-32 


.75 


% 


i' 5 


" 


hi 


71875 


% and 3-32 


.21875 


" 


% and 3-32 


,6875 


% and 1-1<; 


.1ST:. 


" 


V 8 and 1-16 


,65625 


%and i 32 


.15625 


" 


%and 1-32 


,625 


' 


.12.-. 


" 


Vs 


.59375 


& and 3-32 


.09375 


" 


3-32 


.5625 


& and 1-16 


.0625 


" 


1-16 


.53125 

.5 ' 


%and 1-32 


.03125 


" 


1-32 



ONE FOOT OR TWELVE INCITES THE INTEGER. 
9166 equal 11 inches. .1666 equal 2 inches. 



11 inches. 


.Ki.;t; 


10 


.0833 


9 


.<»7L'91 


8 


.0625 


7 " 


.05208 


6 " 


.04166 


5 " 


.03125 


4 


.02083 


3 " 


.01041 



1 

% 

% 

833 7 " .05208 " % 



MENSURATION OF SURFACES. 



Mensuration is that branch of Mathematics which is 
employed in ascertaining the extension, solidities and ca- 
pacities of bodies capable of being measured. 



MENSURATION OF SURFACES. 

To Measure or Ascertain the Quantity of Surface In Any 

Right Lined Figure whose Bides are 

Parallel to Each Other. 

Rule.— Multiply the length by the breadth or perpen- 
dicular higlit, and the product will be the area or superfi- 
cial contents. 
Application of the Rule to Practical Purposes. 

The sides of a square piece of iron are gji inches in 
length, required the area. 

Decimal equivalent to the fraction ]/$ — .875, and 9.875 
X 9.875 = 97.5, etc., square inches, the area. 

The length of a roof is 60 feet 4 inches and its width 
25 feet 3 inches ; required the area of the roof. 

4 inches = .333 and 3 inches = .25 (see table of equiv- 
alents), hence, 60.333 X 25.25 = 1523.4 square feet, the 
area. 



Epitome of Mensuration. 77 

TRIANGLES. 

To Find the Area of a Triangle When the Base and Per- 
pendicular are Given. 

Rule. — Multiply the base by the perpendicular hight 
and half the product is the area. 

The base of the triangle is 3 feet 6 inches in length 
and the hight 1 foot 9 inches ; required the area. 

6 in. = .5 and 9 in. = .75, hence, OD _ = 3.0625 

2 

square feet, the area. 

Any Two Sides of a Right Angled Triangle being Given, to 
Find the Third. 

When the Base and Perpendicular are Given to 
Find the Hypothenuse. 

Add the square of the base to the square of the perpen- 
dicular and the square root of the sum will be the hypothe- 
nuse. 

The base of the triangle is 4 feet and the perpendicular 

3 feet ; then 4 2 + 3- = 25, V25 = 5 feet, the hypothenuse. 

When the Hypothenuse and Base are Given to Find 
the Perpendicular. 

From the square of the hypothenuse subtract the 
square of the base, and the square root of the remainder 
will be the perpendicular. 

The hypothenuse of the triangle is 5 feet and the base 

4 feet ; then 5 2 — 4 2 = 9, and V9 — 3, the perpendicular, 



78 Epitome of Mensuration. 

When the Hypothenuse and Perpendicular are 
Given to Find the Base. 

From the square of the hypothenuse subtract the 
square of the perpendicular, and the square root of the re- 
mainder will be the base. 



OF POLYGONS. 

To Find the Area of a Hegular Polygon. 

Rule. — Multiply the length of a side by half the dis- 
tance from the side to the center, and that product by the 
number of sides; the last product will be the area of the 
figure. 

Example. — The side of a regular hexagon in 12 
inches, and the distance therefrom to the center of the 
figure is 10 inches; required the area of the hexagon. 

— X 12X6 =360 square inches = 2 l / 2 square feet. Ans. 
2 

To Find the Area of a Regular Polygon when the Side Only 

I* Given. 

Rule.— Multiply the square of the side by the multi- 
plier opposite to the name of the polygon in the ninth 
column of the following table, and the product will be the 

area. 

Table of angles re 1 ative to the construction of Regular 
Polygons with the aid of the sector, and of coefficients to 
facilitate their construction without it ; also, of coefficients 



Epitome of Mensuration. 79 

to aid in finding the area of the figure, the side only being 
given. 

! *„ s a - h *S-*i Si i* 

.c o> a> + J o 5 -a ^do °o ° • a 

02 tig "Si S"3 £2* •dS^-dag' g'S 

Names. ^ <<3 ^^^^ <- 

Triangle 3 120 60 .2SS68 1.782 .5773 2. .433012 

Square 4 90 90 .5 1.414 .7071 1.414 1. 

Pentagon 5 72 108 .GSS2 1.175 .8506 1.238 1.720477 

Hexagon 6 60 120 ..S66 1. 1. 1.156 2.598076 

Heptagon 7 513-7 128 4-7 1.0382 .8672 1.152 1.11 3.633912 

Octagon 8 45 135 L2071 .7654 1.3065 1.08 4.828427 

NonagOD 9 40 140 L3737 .684 1.4619 1.06 6.181824 

Decagon 10 36 144 L.53S8 .618 1.618 1.05 7.694208 

Undecagon 11 32 8-11 147 3-11 1.7028 .5634 1.7747 1.04 9.36564 

Dodecagon 12 30 150 1.866 .5176 1.9318 1.037 11.196152 

Note. — " Angle at center" means the angle of radii 
passing from the center to the circumference or corners 
of the figure. " Angle at circumference " means the 
angle which any two adjoining sides make with each 
other. 



THE CIRCLE AND ITS SECTIONS. 
Observations and Definitions. 



i. The circle contains a greater area than any other 
plane figure bounded by the same perimeter or outline. 

2. The areas of circles are to each other as the squares 
of their diameters ; any circle twice the diameter of an- 
other contains four times the area of the other. 

3. The radius of a circle is a straight line drawn from 
the center to the circumference. 

4. The diameter of a circle is a straight line drawn 



8o Epitome of Mensuration. 

through the center and terminating both ways in the cir- 
cumference. 

5. A chord is a straight line joining any two points of 
the circumference. 

6. The versed sine is a straight line joining the chord 
and the circumference. 

7. An arc is any part of the circumference. 

8. A semicircle is half the circle cut off by a diameter. 

9. A segment is any portion of a circle cut off by a 
chord. 

10. A sector is a part of a circle cut off by two radii. 



General Rules in Relation to the Circle. 

1. Multiply the diameter by 3.1416, the product is the 
circumference. 

2. Multiply the circumference by .31831, the product is 
the diameter. 

3. Multiply the square of the diameter by 7854 and the 
product is the area. 

4. Multiply the square root of the area by 1. 12837, tne 
product is the diameter. 

5. Multiply the diameter by .8862, the product is the 
side of a square of equal area. 

6. Multiply the side of a square by 1.128, the product 
is the diameter of a circle of equal area. 

Application of the Rules to Practical Purposes. 
1. The diameter of a circle being 5 feet 6 inches, re- 
quired its circumference. 

5.5 X 3- I 4 I 6 — 17.27880 feet, the circumference. 



Epitome of Mensuration. 81 

2. A straight line or the circumference of a circle being 
17.27880 feet, required the circle's diameter corresponding 
thereto. 

17.27880 X -31831 = 5.5000148280 feet, diameter. 

3. The diameter of a circle is 9^ inches; what is its 
area in square inches? 

9-375 2 = 87-89, etc., X .7854 = 69.029, etc., inches, 
the area. 

4. What must the diameter of a circle be to contain an 
area equal to 69.029296875 square inches ? 

V 69.02929, etc., = 8.3091 X 1-12837 = 9.375, etc., or 
g}i inches, the diameter. 

5. The diameter of a circle is 15^ inches; what must 
each side of a square be to be equal in area to the given 
circle? 

15.5 X .8862 = 13.73, etc., inches, length of side. 

6. Each side of a square is 13.736 inches in length; 
what must the diameter of a circle be to contain an area 
equal to the given square ? 

13736 X 1.128 = 15.49, etc., or 15^ inches, the diameter. 

Any Chord and Versed Sine of a Circle being Given, to Find 
the Diameter. 

Rule. — Divide the sum of the squares of the versed 
size and one-half the chord by the versed sine ; the quo- 
tient is the diameter of corresponding circle. 

7. The chord of a circle equals 8 feet and the versed 
sine equals i l / 2 ; required the circle's diameter. 

8 2 + 1.5 2 = 66.25 -7- 1.5 = 44.16 feet, the diameter. 

8. In the curve of a railway I stretched a line 80 feet 
in length and the distance from the line to the curve I 
found to be 9 inches ; required the circle's diameter. 



82 Epitome of Mensuration. 

8 ° 2 + 75 2 = 640.5625 H-2 = 320.28, etc., feet, the di- 
ameter. 

To Find the Length of Any Arc of a Circle. 

Rule. — From eight times the chord of half the arc 
subtract the chord of the whole arc, and one-third of the 
remainder will be the length, nearly. 

Required the length of an arc, the chord of half the arc 
being 8^2 feet and chord of whole arc 16 feet 8 inches. 

8.5X8 = 68.0 — 16.666 = 5 — 33 ^ = 17.111V, cubic 
feet, the length of the arc. 

To Find the Area of the Sector of a Circle. 

Rule. — Multiply the length of the arc by half the 
length of the radius. 

The length of the arc equals 9J/2 inches and the radii 
equal each 7 inches ; required the area. 

9-5 X 3-5 = 33- 2 5 inches, the area. 

To Find the Area of a Segment of a Circle. 

Rule. — Find the area of a sector whose arc is equal to 
that of the given segment, and if it be less than a semi- 
circle subtract the area of the triangle formed by the 
chord of segment and radii of its extremities ; but if more 
than a semicircle add area of triangle to the area of the 
sector, and the remainder or sum is the area of the seg- 
ment. 

To Find the Area of the Space Coutalned Between Two 
Concentric Circles or the Area of a Circular Ring. 

Rule I. — Mutlply the sum of the inside and outside 
diameters by their difference and by .7854; the product 
is the area. 



Epitome of Mensuration. 83 

Rule 2. — The difference of the area of the two cir- 
cles will be the area of the ring or space. 

Suppose the external circle equal 4 feet and the in- 
ternal circle 2 l /> feet, required the area of space contained 
between them or area of a ring. 

4 + 2.51=6.5 and 4 — 2.5=1.5, hence, 6.5 X 1.5 X 
.7854 = 7.65 feet, the area ; or, 

The area of 4 feet is 12.566; the area of 2.5 is 4.9081. 
(See table of areas of circles.) 

12.566 — 4.9081 = 7.6579, the area. 

To Find the Area of an Ellipse or Oval. 

Rule. — Multiply the diameters togther and their prod- 
uct by .7854. 

An oval is 20 x 15 inches, what are its superficial con- 
tents ? 

20 X 15 X 7854 = 235.62 inches, the area. 

To Find tiie Circumference of an Ellipse or Oval. 

Rule. — Multiply half the sum of the two diameters by 
3.1416 and the product will be the circumference. 

Example. — An oval is 20 x 15 inches, what is the cir- 
cumference. 
20+ 15 



2 
ference. 



= 17.5 X 3-1416= 54.978 inches; the circum- 



OF CYLINDERS. 

To I in. I ih. Convex Surface of a Cylinder. 

Rule. — Multiply the circumference by the flight or 
length, the product ivill be the surface. 

Example. — The circumference of a cylinder is 6 feet 



84 Epitome of Mensural 



ion. 



4 inches and its length 15 feet, required the convex sur- 
face. 

6-333 X 15 = 94-995 square feet, the surface. 



OF CONES AND PYRAMIDS. 

To Find the Convex Surface of a it i- in Cone or Pyramid. 

Rule. — Multiply the circumference of the base l\r the 
slant hight and half the product is the slant surface; if the 
surface of the entire figure is required, add the area of the 
base to the convex surface. 

Ex \milk. — The base of a cone is 5 feet diameter and 
the slant hight is 7 feet, what is the convex surface? 
5 X 31416 = 15. 7Q circumference of the base and 

1 ^ 70 yc 7 

- = 54.95 square feet, the convex surface. 

To Find the Convex Surface of a Fruatum of a (one or 
Pyramid. 

Rule. — Multiply the sum of the circumference of the 
two ends by the slant hight and half the product tvili be the 
slant surface. 

The diameter of the top of the frustum of a cone is 
3 feet, the base 5 feet, the slant hight 7 feet 3 inches ; re- 
quired the slant surface. 

2s 12 X 72s 

9.42 + 15.7 = — /- = 91.06 square feet, slant 

surface. 



Epitome of Mensuration. 85 

OF SPHERES. 

To Find the Convex Surface of a Sphere or Globe. 

Rule. — Multiply the diameter of the sphere by its cir- 
cumference and the product is its surface; or, 

Multiply the square of the diameter by 3.1416; the 
product is the surface. 

What is the convex surface of a globe 6 l / 2 feet in di- 
ameter? 

6.5 X 3-i4i6 X 6.5 = 132.73 square feet; or, 6.5 2 = 
42.25 X 3-i4i6 = 132.73 square feet, the convex surface. 



MENSURATION OF SOLIDS AND CAPACITIES 
OF BODIES. 

To Find Ihe Solidity or Capacity of Any Figures In the 
Cubical Form. 

Rule. — Multiply the length of any one side by its 
breadth and by the depth or distance to its opposite side, 
and the product is the solidity in equal terms of measure- 
ment. 

Example. — The side of a cube is 20 inches ; what is its 
solidity? 

20 X 20X 20 = 8000 cubic inches, or 4.6296 cubic 
feet, nearly. 

A rectangular tank is in length 6 feet, in breadth 4 l / 2 
feet and its depth 3 feet ; required its capacity in cubic 
feet ; also its capacity in United States standard gallons. 

6X4.5X3 = 81 cubic feet; 81 X 1728 = 139,968 -f- 
231 = 605.92 gallons, 



86 Epitome of Mensuration. 

OF CYLINDERS. 

To Find the Solidity of Cylinders. 

Rule. — Multiply the area of the base by the hight and 
the product is its solidify. 

Example. — The base of a cylinder is 18 inches and 
hight 40 inches; 

18 2 X 7854 X 4 n = 10.178.7840 cubic inches. 

To Find the Contents In Gallons of Cylindrical Vessels. 

Rule. — Take the dimensions in inches and decimal 
parts of an inch. Square the diameter, multiply it by the 
hight, then multiply the prod net by .0034 for wine gallons. 
or by .002785 for beer gallons. 

Example. — How many United States gallons will a 
cylinder contain whose diameter is [8 inches and length 
30 inches ? 

18- X 30 = 97 2 o X -0034 = 33.04. etc., gallons. 



OF CONES AND PYRAMIDS. 

To Find the Solidity of a tone or a Pyramid. 

Rule. — Multiply the area of the base by the perpen- 
dicular hight and one-third the prod net will be the solidity. 

Example. — The hast- of a cone is j ! .j feet and the 
hight is 3M feet, what is the solidity? 

2.2s 2 X 7854 X 3-75 „ .: f 4 rf 
— - = 4-97 cubic feet, the solidity. 



Epitome of Mensuration. 8 7 

To Find the Solidity of the Frustum of a Cone. 

R ULE . — Jo the product of the diameters of the ends 
add one-third the square of the difference of the diame- 
ters; multiply the sum by .7854 a ' ui t,lc product will be the 
mean area between the ends, which multiplied by the per- 
pendieular hight of frustum gives the solidity. 

Example. — The diameter of the large end of a frus- 
tum of a cone is 10 feet, that of the smaller cud is 6 feet 
and the perpendicular hight 1 2 feet, what is its solidity? 

I0 6 = 4 2 =i6-i- 3= 5-333 square of difference of 

ends ; and 10X6 + 5.333 = 65-333 X 7854 X 12 = 
615.75 cubic feet, the solidity. 

To Find the < oiitent* in I . 8. Standard Gallons of the 
Frustum of a Cone. 

r ule . — Jo the product of the diameters, in inches and 
deeimal parts of an inch, of the ends, add one-third the 
square of the difference of the diameters. Multiply the 
sum by the perpendicular hight in inches and decimal parts 
of an inch and multiply that prod net by .0034 for wine 
gallons, and by .002785 for beer gallons. 

Example.— The diameter of the large end of a frus- 
tum of a cone is 8 feet, that of the smaller end is 4 feet and 
the perpendicular hight 10 feet; what are the contents in 
United States standard gallons? 

96 — 48 = 48' = 2304 -f- 3 = /68 ; 96 X 48 + 768 = 
5376 X 120 X .0034 = 2193.4 gallons. 

To Find the Solidity of the Frustum of a Pyramid. 

Rule. — Add to the areas of the two ends of the frus- 
tum the. square root of their product, and this sum multi- 



88 Epitome of Mensuration. 

plied by one-third of the perpendicular hight will give the 
solidity. 

Example. — What is the solidity of a hexagonal pyra- 
mid, a side of the large end being 12 feet, one of the 
smaller ends 6 feet and the perpendicular hight 8 feet ? 

374.122 X 93-53 = v 34,99i-63 = ^7-o6. 17+122 + 

93-53 + 187.06= ^321 ><_§ = 1745.898 cubic feet, 

solidity. 

To Find the Solidity of a Sphere. 

Rule. — Multiply the cube of the diameter by .5236 
and the product is the solidity. 

Example. — What is the solidity of a sphere, the di- 
ameter being 20 inches ? 
20 3 = 8000 X -5236 = 4188.8 cubic inches, the solidity. 



TABLES, RULES AND RECIPES. 



BLACK SHEET IRON. 

Black Sheets are rolled to the following Standard Ganges adopted 

by the United States, taking effect July 1, 1893. 

, THICKNESS. > , WEIGHT. ^ 

Approxi- 

Approximate mate thick- Weight per Weight per 

thickness ness in dec- square foot square foot 

Number infractions imal parts in ounces in pounds 
of gauge. of an inch, of an inch, avoirdupois, avoirdupois. 

10 9-64 .140625 90 5.625 

11 1-8 .125 80 5. 

12 7-04 .109375 70 4.375 

13 3-32 .09375 60 3.75 

14 5-04 .0781 25 50 3.125 

15 9-128 .0703125 45 2.8125 

16 1-16 .002.-, 40 2.5 

17 9-160 .05625 36 2.25 

18 1-20 .05 32 2. 

19 7-160 .04375 28 1.75 

20 3-80 .0375 24 1.50 

21 11-320 .< 134375 22 1.375 

22 1-32 .03125 20 1.25 

23 9-320 .028125 18 1.125 

24 1-40 .025 16 1. 

25 7-320 .( >21875 14 .875 

20 3-160 .01875 12 .75 

27 11-640 .0171875 11 .6875 

28 1-64 .015625 10 .625 

29 9-640 .0140625 9 .5625 

30 1-80 .0125 8 .5 

31 7-040 .0109375 7 .4375 

32 13-1280 .0101 5625 6V 2 .40625 

A variation of 2% per cent, either way is allowed. 

Plate Iron. 

The following table gives the weight per square foot 

for iron plates 1-16 inch up to Y / 2 inch thick. 

Thickness. Weight in lbs. Thickness. Weight in lba. 

1-16 2.50 > 5-16 12.50 

1-8 5.00 3-8 15.00 

3-16 7.50 7-16 17.50 

1-4 10.00 1-2 20.00 



Tables, Rules and Recipes. 
WEIGHT OF SHEET LEAD. 

The thickness of lead is in common determined or understood by the 
weight, the unit being that of a square or superficial foot ; thus : 

4 lbs. lead is 1-16 inch in thickness ; 6 do. 1-10 do. ; 7y a do. 1-8 do. ; 11 
do. 3-16 do. ; 15 do. 1-4 do. 



DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF A 

POUND. 



03125 


%o 


z. .28125 


4% 08. 


.53125 


S% oz. .78125 


12% 


0625 


1 


.3125 


5 " 


.5623 


9 ' 


.8125 


13 


00375 


1% * 


.34375 


f,i . ■■ 




9Vj ' 


84375 


13Mi 


125 


2 ' 


.375 


6 •• 


,625 


10 • 


.ST.". 


14 


L5625 


2% 


.40625 


.;i, •• 


.65625 


1MI, • 


' 


14'... 


1875 


3 ' 


a.;::, 


7 " 


.6875 


11 ' 


.9375 


15 


21875 


3% 


.46875 


7% '• 


.71875 


11% ' 


.96875 


15% 


25 


4 ' 


.5 


8 " 


.75 


1-' ' 


1. 


16 



DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF AN 
INCH WHEN DIVIDED [NTO 32 TARTS; LIKEWISE nil-: 
DECIMALS EQUIVALENT TO THE FRACTIONAL PARTS OF 
A FOOT. 





Parts of an 




Parts of an 




Parts <>f 


Decimals. 




inch. 


Decimals. 


inch. 


Decimals. 


a foot. 


.03125 


1-32 




.53125 


'..and 1-32 


.<Hil41 


% 


.0625 


1-16 




.5625 


».. and 1-16 


.02083 


V* 


.09375 


3-32 




.59375 


' a and 3-32 


.03125 


% 


.125 


V s 




.626 


% 


.04166 


y a 


.15625 


% 


and 1-32 


.65625 


% and i 32 


.05208 




.1875 


% 


and 1-16 


,6875 


■". and L-lfi 


.0625 


% 


.21875 


% 


and 3-32 


.71875 


% and 3-32 


.07291 


% 


.25 


% 




.75 


% 


.0833 


i 


.28125 


V* 


and 1-32 


.7S125 


-, and 1-32 


.1666 


2 


.3125 


'•J 


and 1-16 


.8125 


% and 1-16 


.25 


3 


.34375 


K 


and 3-32 


.84375 


% and 3-32 


.3333 


4 


.375 


% 




.S75 


% 


.4166 


5 


.40625 


% 


and 1-32 


.90625 


T s and 1-32 


.5 


6 


.4375 


% 


and 1-16 


.9375 


T s and 1-16 


.5833 


7 


.46875 


% 


and 3-32 


.96875 


7 . and 3-32 


.6666 


8 


.5 


% 




1. 


1 inch. 


.75 

.8333 

.9166 


9 

10 
11 



Tables, Rules and Recipes. 91 

TO ASCERTAIN THE WEIGHTS OF PIPES OF VARIOUS METALS, 
AND ANY DIAMETER REQUIRED. 

Thick. Wrought Thick. Wrought 

Inch. iron. Copper. Lead. Inch. iron. Copper. Lead. 

1-32 .326 .38 .483 1.027 1.9 2.417 

1-16 .653 .76 .967 3-16 1.95 2.28 2.9 

3-32 .976 1.14 1.45 7-32 2.277 2.66 3.383 

1-8 1.3 1.52 1.933 1-4 2.6 3.04 3.867 

Rule. — To the interior diameter of the pipe, in inches, 
add the thickness of the metal; multiply the sum by the 
decimal number opposite the required thickness and under 
the metal's name; also by the length of the pipe in feet; 
and the product is the weight of the pipe in pounds. 

I. Required the weight of a copper pipe whose in- 
terior diameter is 2 l / 2 inches, its length 20 feet, and the 
metal % inch in thickness. 

2.25 + .125 = 2.375 X 1.52X20 = 72.2 pounds. 



WEIGHT OF GALVANIZED SHEETS. 

Ounces per Ounces per Ounces per 

square foot. square foot. squarefoot. 

No. 14 52% No.20 26% No. 26 L4% 

No. 15 47% No. 21 24% No. 27 L3% 

No. If, 42% No. 22 22% No. 28 12% 

No. 17 38% No. 23 20% No. 29 11% 

No. 18 34 V. No. 24 18% No. 30 10% 

No. 19 30 % No. 25 16% 



ORDINARY DIMENSIONS OF GALVANIZED SHEETS. 

Widths 40 38 36 34 32 30 28 2G 24 22 20 

Gauges. Lengths. 

No. 14 00 90 96 96 00 00 00 00 96 

Nos. 10 to 22 120 120 120 120 120 120 120 120 120 120 120 

Nos. 23 and 24. . . 06 90 00 00 108 120 120 120 120 108 108 

Nos. 25 to 28 90 90 108 120 120 120 120 108 108 

Nos. 29 and 30 90 96 00 00 . . . . 



92 



Tables, Rules and Recipes. 



SIZES OF TIN WARE IN THE FORM OF FRUS- 
TUM OF A COXE. 



PANS. 



Size. 
20 qt. 

16 ■• 

14 " 

in •• 
6 " 


Diam. 
of top. 

19V.. in. 

is ■• 

15*5 - 

14% " 
12% - 


Diam. 
of bot. 
13 in. 

ID, - 

11 " 

9 " 


Ilight. 
8 in. 

f.i, •• 
.;>, •• 
4% - 


Size. 
2qt. 

3pt. 
1 " 
Die 


Diam. 

of top. 

9 in. 
8% - 
6% - 
9 " 


Diam. 
of bot. 
6 in. 

4 " 
7', " 


Ilight 
3% in. 

2% - 
1% " 






DISH 


KETTLES 


A XI) I 


'AILS. 






Size. 
14 «)t. 
10 " 


Diam. 
of top. 
13 in. 
11% - 


Diam. 

of bot. 

9 in. 

7 


Bight 

9 in. 

COFFEE 


Si/.'. 
ti.|t. 
■ > .. 

POTS. 


Diam. 

of top. 

9% in. 


Diam. 
of bot. 
5% in. 

4 • 


Hight. 

6% in. 
4 " 


Size. 

lgal. 


Diam. 
»if top. 

1 in. 


Diam. 
of bot. 

7 in. 


Hight. 

8% in. 


Six.-. 

:; qt. 


I Ham. 

of toll. 

3% in. 


I Main. 

of hot. 

6 in. 


Ilight. 
8% in. 








WASH BOWLS. 








Size 
Large wash bowl 

in] i * ■ 1 1< i •> ■' 








l Ham. 

..f top. 

. 11 in. 
11 
9% - 


Diam. 
of bot. 

.-,'•, in. 


Hight. 

5 in. 










Small 

Milk - 


wash bowl 

if ralner . . . 
















DIPPERS. 








Size. 

% gal. 


Diam. 
of top. 

6% in. 


Diam. 
of bot. 

4 in. 


Hight. 

1 in. 


Size, 
lpt. 


Diam. 
of top. 

1', in. 


Diam. 
of bot. 
3* in. 


Highl 

2$ in. 








MEASURES. 








Size. 
1 gal 

',■ ' 

1 qt. 


Diam. 
of top. 

. 5% In. 

4 " 
3% •• 


Diam. 
of bot. 

C'.in. 
1% - 
4 


Right. 

In. 

g ■« 


Size. 
i pt. 


Diam. 

of top. 

2% in. 
2% ■ 


Diam. 

of Lot. 
::•-, in. 
2% - 


Ilight 
4% in 
3% " 




druggists' and liquob 


: dealers' measures 




Size. 
5 gal. 
3 " 
2 " 
1 " 


Diam. 
of top. 

8 in. 
7 •• 
6 " 
3% " 


1 Ham. 
of bot. 

13% in. 

11 1.. '• 

io% •• 


Hight. 

12% in. 
10% - 

8% " 

7% '• 


Size. 
%gal. 

i" -it. 
l pt. 


Diam. 

of top. 
3% in 
2% - 
2 " 
1% " 


Diam. 
of bot. 
6% in. 

4 " 
3% " 


Hight. 

6 in. 
4% - 
4 " 
3% " 



Tables, Rules and Recipes. 



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Tables, Rules and Reap 



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Tables, Rules and Recipes. 



RELATIVE WEIGHTS OF ALUMINUM AND 
COPPER SHEETS. 

ROLLED AHJUIINITUI has a specific gravity of 2.72. One cubic foot 
weighs 169 T 5 5 W lbs. One square foot of one inch thick weighs U^%% lbs. 
Rolled Copper is 3.283 times heavier than similar sections of Rolled 
Aluminum. 



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9.75 


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36 


11.00 


48 


14.70 


18 


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40 


12.20 


11.66 3.56 20 


6.10 


31.25 


9.52 


45 


13.75 


60 


18.30 


16 


.0645 


48 


14.65 


14 4.2 


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7.32 


37.50 


11.45 


54 


16.50 


72 


22.00 


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17.10 


16.33 4.98 28 


8.53 


43.75 


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63 


19.20 


84 


25.60 


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9.75 


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15.30 


72 


21.95 


96 


29.30 


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70 


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35 


10.70 


55 


16.80 


79 


24.10 


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32.00 


12 


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81 


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12.40 


63 


19.20 


91 


27.75 


122 


37.20 


11 


.120 


89 


27.15 




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13.60 


70 


21.35 


100 


30.50 


134 


40.85 


10 


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100 


30.50 




50 


15.30 


78 


23.80 


112 


34.20 


150 


45.70 


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16.80 


86 


26.20 


124 


37.80 


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61 


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96 


29.30 


138 


42.10 


184 


56.10 


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118 


36.00 


170 


51.80 


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184 


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246 


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177 


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138 


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199 


60.70 


266 


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96 


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217 


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289 


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174 


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251 


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253 






1261/o 


38.60 


198 


60.40 


285 


86.90 


380 


116.00 



One ounce per square foot aluminum sheet is 0.0044 inch thick and 
corresponds to about No. 37 B. & S. gauge. 



Tables, Rules and Recipes. 



97 



SHEET COPPER. 

Official table adopted by the Association of Copper Manufac- 
turers of the United States. 

Rolled copper has specific gravity of 8.93. One cubic foot 
weighs 558 12 7iooo pounds. One square foot, of 1 inch thick, weighs 
46 51 /ioo pounds. 



6C .2 Oj 

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35 00537 

33 00806 

31 0107 

29 0134 

27 0161 

26 0188 

24 0215 

23 0242 

22 0269 

21 0322 

19 0430 

18 0538 

16 0645 

15 0754 

14 0860 

13 095 

12 109 

11 120 

10 134 

9 148 

8 105 

7....... .180 

6 203 

5 220 

4 238 

3 259 

2 284 

1 300 

340 



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6 

8 
10 

12 
14 
16 

18 

20 

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56 

64 

70 

81 

89 

100 

110 

123 

134 

151 

164 

177 

193 

211 

223 

253 



£* 

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11.66 

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16.33 

18.66 



2S i 



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2 
3 
4 
5 

6 

7 
8 
9 

10 

12 

16 

20 

24 

28 

32 

35 

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50 

55 

61 

67 

75y 2 

82 

88 1/ 2 

96 

105i/o 
111% 
1261/2 



C SQ 
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4.68 

6.25 

7.81 

9.37 

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12.50 

11.06 

15.62 

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31.25 
37.50 
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63 
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78 
86 
96 

105 

118 

128 

338 

151 

165 

174 

198 



5.2 

CO-w 
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tit 

4.50 
6.75 
9 

11.25 

13.50 

15.75 

18 

20.25 

22.50 

27 

36 

45 

54 

63 

72 

79 

91 
100 
112 
124 
138 
151 
170 
184 
199 
217 
238 
251 
285 






4 j *r 

Of 4* 

6 

9 

12 

15 

18 

21 

24 

27 

30 

36 

48 

60 

72 

84 

96 

105 

122 

134 

150 

165 

184 

201 

227 

246 

266 

289 

317 

335 

380 



TABLES 

OF THE 

CIRCUMFERENCES OF CIRCLES, 

TO THE 

Nearest Fraction of Practical Measurement; 
also, 

the areas of circles, in inches and decimal parts, 

likewise in felt and decimal parts, as 

may be required. 



Rules that may render the following tables more gen- 
erally useful. 

1. Any of the areas in inches, multiplied by .052, or 
the areas in feet multiplied by 7.48, the product is the num- 
ber of gallons at 1 foot in depth. 

2. Any of the areas in feet, multiplied by .03704, the 
product equals the number of cubic yards at 1 foot in 
depth. 



Dia. in 


Circum. 


Area in 


Side of 


Dia. in 


Cir. 


in Area 


in Area in 


inch. 


in inch. 


sq. inch. 


= sq. 


inch. 


ft. 


in. sq. Inch. sq. ft. 


1-16 


.196 


.0030 


.0554 


1 in. 


3% 


7v, 4 


7 /s 


l 8 


.392 


.0122 


.1107 


Lfc 


:;>., 


.9940 


% and 3-32 


3-36 


.589 


.0276 


.1661 


W4 


3% 


1.227 


1 in. 


1-4 


.785 


.0490 


.2115 


3 


414 


1.484 


1 3-16 


5-16 


.981 


.0767 


.2669 


4% 


1.707 


1 5-16 


3-8 


1.178 


.1104 


.3223 


1% 


5V 8 


2.074 


1 7-16 


7-16 


1.374 


.1503 


.3771 


1% 


5% 


2.405 


1 9-16 










1 7 > 


5% 


2.761 


1 11-16 


1-2 


1.570 


.1963 


.4331 


2 in. 


6^4 


.°..141 


1% 


9-16 


1.767 


.2485 


.4995 


2% 


O-'s 


3.546 


l 7 /s 


5-8 


L963 


.3068 


.5438 


- 1 . 


7 


3.976 


2 in. 


11-16 


2.159 


.3712 


.6093 


2% 


7% 


4.430 


2y 8 


3-4 


2.356 


.4417 


.6646 


J'., 


T ; . 


1.111 IN 


2 3-16 


13 16 


2 552 


.5185 


.7200 


2^ 


8V4 


5.412 


2 5-16 


7-8 


2>48 


.6013 


.7754 


2% 


8% 


5.939 


2 7-16 


15-16 


2.945 


.0903 


.8308 


2% 


9 


6.491 


2 9-16 



Tables, Rules and Recipes. 



99 



Dia. 


in. Cir 


. Area in 


Side of 


Dia. in 


Cir. in 


Area in 


Area in 


inch, in inch sq. 


inch. 


= sq. 


inch. 


ft, 


. in. 


sq. inch. 


sq. ft. 


3 in 


9% 


7.( 


)68 2% 


10 in. 


2 


7% 


78.540 


.5497 


3% 


»% 


7. 


669 2% 


ioy 8 


2 


7% 


80.515 


.5636 


3V4 


10% 


8.295 2% 


ioy 4 


2 


8% 


82.516 


.5776 


3% 


10% 


s.940 3 in. 


10% 


2 


8% 


84.540 


.5917 


3y 2 


11 


9.62] 3y 8 


ioy 2 


2 


8% 


86.590 


.6061 


3% 


11% 


10.320 3y 4 


10ft 

10% 


2 


9% 


88.664 


.6206 


3% 


11% 


11.044 3% 


2 


9% 


90.762 


.6353 


3% 


12% 


11. 


793 2 


17-16 


10% 


2 


10% 


92.855 


.6499 


Dia. 

incl 
4 in. 
4% 

4i/4 
4% 

41/2 
4% 
4% 


in Cir. in 

1. ft. in. 

1 oy 2 

1 0% 

1 1% 
1 1% 
1 2% 
1 2% 
1 2% 


Area in 
sq. inch. 
12.566 
13.364 
14.186 
15.033 
15.904 
16.800 
L7.720 


Area in 
sq. ft. 
.0879 
.0935 
.0003 
.1052 
.1113 
.1176 
.1240 


11 in. 

11% 

11% 

11% 

11% 

11% 

11% 

11% 


2 
2 
2 
2 
3 
3 
3 
3 


10% 
10% 

11% 
11% 

0% 
0% 
0% 
1% 


95.033 
97.205 
99.402 
101.623 
103.869 
106.139 
108.434 
110.753 


.6652 
.6874 
.6958 
.7143 
.7290 
.7429 
.7590 
.7752 


4% 


1 


3% 


18.665 


.1306 






















12 in. 


3 


1% 


113.097 


.7916 


5 in. 


1 


3% 


L9.63S 


.1374 


12% 


3 




115.466 


.8082 


5% 


1 


4's 


20.629 


.1444 


12% 


3 


2% 


117.859 


.8250 


5% 


1 


4y, 


21.647 


.1515 


12% 
L2% 
12% 


3 


2% 


120.276 


.8419 


5% 


1 


4% 


22.690 


.15.S.S 


3 


3% 


122.718 


.8590 


5V 3 


1 


5% 


23.758 


.1 •;»;:•, 


3 


3% 


125.185 


.8762 


5% 


1 


5% 


24.850 


.1739 


12% 


3 


4 


127.676 


.8937 


5% 


1 


6 


25.967 


.1817 


12% 


3 


4% 


130.192 


.9113 


5% 


1 


6% 


27.108 


.1897 






















13 in. 


3 


4% 


132.732 


.9291 


6 in. 


1 


6% 


28.274 


.1070 


13% 
1314 


3 


5% 


135.207 


.0470 


6% 


1 


7% 


29.464 


.2062 


3 


5% 


137.886 


.0642 


»>', 


1 


7% 


.••.(MIT!) 


.2147 


13% 


3 


6 


140.500 


.9835 


6% 


1 


8 


31.919 


.2234 


131/2 


3 


6% 


143.139 


1.0019 


6% 


1 


8% 


33.183 


.2322 


13% 


3 


6-Yt 


145.802 


1.0206 


ti% 


1 


V S 


34.471 


.2412 


13% 


3 


7% 


148.489 


1.0294 


• »". 


1 


9% 


3.-.. 784 


.2504 


13% 


3 


7% 


151.201 


1.0584 


6% 


1 


9% 


37.122 


.2508 






















14 in. 


3 


7% 


153.938 


1.0775 


7 in. 


1 


10 


38.484 


.2693 


14% 


3 


8% 


156.699 


1.0968 


7% 


1 


10% 


39.871 


.2791 


14% 


3 


8% 


159.485 


1.1193 


7% 


1 


10% 


41.282 


.2889 


14% 


3 


9% 


162.295 


1.1360 


7% 


1 


11% 


42.718 


.2900 


14% 


3 


9% 


165.130 


1.1569 


7% 


1 


11% 

11% 


44.178 


.3092 


14% 


3 


9% 


167.989 


1.1749 


7% 


1 


45.663 


.3196 


14% 


3 


ioy 4 


170.873 


1.1961 


7% 

7% 


2 


0% 
0% 


47.173 

47.707 


.3299 
.3409 


14% 


3 


10% 


173.782 


1.2164 


8 in 

8% 


2 
2 


1% 

1% 


50.265 

51.848 


.3518 
.3629 


15 in. 

15% 


3 
3 


11% 
11% 


176.715 
170.672 


1.2370 
1.2577 


si; 


2 


1% 


53.456 


.3741 


15% 


3 


11% 


182.654 


1.2785 


8% 


2 


2% 

2% 


55.088 


.3856 


15% 


4 


0% 


185.661 


1.2996 


8V 2 


2 


56.745 


.3972 


15% 


4 


0% 


188.692 


1.3208 


8% 


2 


a 


58.426 


.4089 


15% 


4 


1 


191.748 


1.3422 


8% 


2 


3% 


60.132 


.4209 


15% 


4 


1% 


194.828 


1.3637 


8% 


2 


3% 


61.862 


.4330 


15% 


4 


1% 


197.933 


1.3855 


in. 


2 


4% 


63.617 


.4453 


16 in. 


4 


2% 


201.062 


1.4074 


9% 


2 


4% 


65.396 


.4517 


16% 


4 


2% 


204.216 


1.4295 


9% 


2 


5 


67.200 


.4704 


iey 4 


4 


3 


207.394 


1.4517 


0% 


2 


5% 


69.029 


.4832 


16% 


4 


3% 


210.597 


1.4741 


'i!.', 


2 


5% 


70.882 


.4961 


H£ 


4 


3% 


213.825 


1.4967 


9% 


2 


6% 


72.750 


.5003 


16% 


4 


217.077 


1.5195 


03; 





fi% 


74.662 


.5226 


16% 


4 


4% 


220.353 


1.5424 


9% 


2 


7 


76.588 


.5361 


16% 


4 


5 


223.654 


1.5655 



IOO 



'fables, Rules and Recipes. 



I>ia. in 


Cii 


\ in 


Area in 


Area in 


Dla. In 


Cir. 


in 


Area in 


Area in 


Inch. 


ft. 


in. 


bq. Inch. 


Bq. ft. 


ft. 


in. 


ft. 


in. 


sq. Inch. 




17 in. 


4 




226.980 


1.5888 


•J. 





«; 




152.290 


3.1418 


17', 


4 




230.330 


1.6123 


2 


0% 


6 




461.864 


3.2075 


17V4 


4 


G% 


233.705 


L.6359 


L' 




6 




iti 136 


3.2732 


IT % 


4 


6% 


237.104 


1.6597 


_ 




6 




181.106 


3.3410 


IT'... 


4 


.;: 


240.528 




■J. 


l 


♦; 




190.875 


3.4081 


1 J% 


4 




243.977 


1.7078 


•> 


1% 


6 




500.741 


3.47 i 5 


17% 


4 


7% 


247.450 


L.7321 


2 




6 


M. 


510.706 


3 5468 


17% 


4 


8% 


250.947 


1.7566 


•J. 


i -. 


6 




520.769 


3.6101 


is in. 


4 


8% 


254.469 


1.7812 


2 


• > 


6 




530.930 


3.6870 


18% 


4 


8% 


258.016 


1 B061 


2 




6 


10% 


541.189 


3.7583 


18% 


4 




261.587 


1.831 1 


2 




6 


11', 


551.547 


:; 8302 


1^'s 


1 


265 182 




2 


2% 


7 





562.002 


3.9042 


LS% 


1 


10% 




1.8816 


2 




7 




:.72. :.:.<; 


:; 9761 


1 8% 


4 


10% 


272.4 17 


1.9071 


2 


3% 


T 


1 * 


583.208 


4. <>:,( id 


18% 


4 


10% 


276.117 




1 


T 




593.958 


1.1241 


L8% 


4 


11'. 


279.811 




- 




7 




604.807 


L2 • 


19 In. 


1 


11% 


283.529 


1 '..-IT 


•■ 


i 


7 




615.753 


L2760 


19% 


5 





287 272 


1 9941 


2 


4% 


7 




626.798 


1.3521 








291 039 


2 0371 


2 


7 


637.941 


I 1302 




5 






2.0637 


•_> 




7 


6% 


649.182 


1 5083 


19% 


5 


1', 


298 648 


2.090 t 


2 




7 


7 


660.521 




5 


1% 


302. 189 


2.1172 


2 




T 




671 958 


\ 6665 


I 1 .", 




2 




2 1 l 1 ■: 


2 


5% 


7 




683. 194 


I 7467 


19% 


5 




310.245 


2.1716 


2 




T 


9% 




i B27 t 


20 Id 


g 


2% 


31 1.160 


2.1990 


2 




7 


10% 




i 9081 


20% 


5 


3% 


318 099 


2 2265 


•j 




7 


i l 


718.690 


1.9 -'I 


20% 


r, 




322 063 


2.2543 


2 




T 


l L% 


r.-.n 618 


5 0731 




r> 


i 


326.051 


•J 2822 


2 




B 


0% 


742.644 


5.1573 




5 




330.064 


2 3103 


2 


T 


S 




Tr.4.T«;;» 




5 




334 L01 




2 


7% 


- 








20% 


5 


5% 


338.163 


2.3670 


o 


7', 


8 




779.313 


5 Ml 'J 


20% 


5 


5% 


342.250 


2.3956 


2 








791.732 




21 in. 


5 




346 361 


2 124 i 


1! 


8 


B 


4% 


804.249 




21% 


5 




350 197 


2 1533 


•« 


8% 






816.865 




-1'. 


K 




:;:. 1 657 


2.4824 


2 


8 


6$ 




5.7601 


21% 


C 


7% 


358 841 


2.51 IT 


•j 


- i 


B 


6% 




5 8491 


21% 


5 


7% 


363.051 


2 5 1 1 2 


2 




B 




855.300 




21% 


5 


7 T - 


367.284 


2.5708 


'J 




B 






6.0291 


21% 


5 


8% 


371 543 


2.6007 


•i 




8 


881.415 


6.1201 


21% 


5 




375.826 


2.6306 


2 


8 


10 


B94.619 


6.2129 


22 in. 


5 


9% 


380.133 




•_> 


1ii 






907.922 




22% 


5 


9% 


38 l. 165 


2.6691 


•_> 




- 


11% 


921.323 


6.3981 


22% 


5 




388.822 


2.7016 


;_> 


10% 


9 




934.822 


6.491 1 




5 


10% 


393 203 


2.7224 


•> 


10% 


9 


1% 


948.419 


6.5863 


22iZ 


5 


10% 


397.608 


2.7632 


2 


11 


9 


i T - 


962.115 


6.6815 


22% 


5 


11 


402 038 


2.7980 


•. 


11% 


9 




975.908 


6 7772 


22% 


5 


1 1' . 


106. 193 


2.8054 


•j 


1 1% 


:» 


3% 


989 800 




■'" 7 . 


5 


Ll% 


410.972 


2.8658 


•j 


1 L% 




4% 


1003.79 


6.9701 


23 in. 


6 


0% 


415.476 


2.8903 


3 


<» 


9 


5 


1017.87 


T 0688 


23% 


6 


0% 


120.004 


2 9100 


3 


0% 


9 




1032.06 


7.1671 




6 


1 


424.557 


2.9518 


3 


0% 


9 




L046.35 


7.2664 








429.135 


2.9937 


3 




9 


7% 


1060.73 


7.3662 


23% 


6 




433.737 


3.0129 


3 


1 


9 




1075.21 


T 1661 




6 






3.0261 


3 


1% 


9 


9 


1089.79 


7.5671 


23% 


6 


2% 


443.01 1 


n.« »Tl2_i 


3 


1% 


9 


9% 


1104.46 


7.6691 


23% 


6 


8 


447.600 


3.1081 


3 




9 


10% 


1110.24 


7.7791 



Tables, Rules and Recipes. 



ioi 



Da. in Cir. in Area in Area in 



ft 



sq. inch. sq. ft. 



2% 

- ; » 

3 

3% 



i» ii* s 1134.12 7.st;si 



6 



7% 
7% 

7% 



8% 
9 



9% 

to 

10% 
10% 

10% 

11 

111, 
111, 

Ll% 



4 in 

4', 10 

-1>, L0 

Ki 

:,', 10 

:,'., L0 

.-.■••■; 10 



6% n 
6% 11 



l l 
11 
n 
l l 



8 11 

8% 11 



9% ii 



i i 
1 1 

12 
12 

\-i 
12 
12 
12 
12 
12 



112 
0% 12 
0% 12 
0% 12 

1 12 
T, 12 
T, 12 
t% 13 

2 13 
2% 13 

-i, 13 

2% 13 

3 13 
3% 13 
3% 13 
3% 13 



0% 

1 -, 
2% 
3% 

4 
4". 



1149.09 
1164.16 
1179.32 
l 194.59 
1209.95 
1225. 12 
1240.98 



5% 1256.64 

6 & 121 

I', 1288 25 
1304.20 
1320.25 
1336.40 
1352.65 
1369.00 



9% 

11% 



11% 

0% 

i ; 
-", 

3 

6% 

7 

10% 
10% 
Ll% 

.i'.. 

i* 

4% 

;;'' 

6% 

7'.. 

9% 
9% 

io4i 

11% 

0% 

1 

l 7 - 

2y 2 

t A 

5% 

ey 3 



1385.4 1 
1 101.98 
l 118.62 
1 135 36 
1452.20 
1 169.1 l 
l isf.. 17 
1503 30 

1530.53 

1555.28 
1572.81 
1590. 13 
1608.15 
1625.97 
1643.89 

1661.90 
1680.02 
1698 23 
1716.54 
1734.94 
1753. 15 
1772.05 
1790.76 

1809.56 
1828.46 
1847.45 
1866.55 
1885.74 
1905.03 
1924.42 
1943.91 

1963.50 

1983.18 
2002.96 
2022.84 
2042.82 
2062.90 
2083.07 
2103.35 



7.9791 

8.0846 
8.1891 
8.2951 
8.4026 
8.5091 
8.6171 

8.7269 
8.8361 
8.9462 
9.0561 
9.1686 
9 21 12 
9.3936 
9.5061 

9.6212 
9.7364 
9.8518 
9.9671 
10.084 
10.202 
10.320 
L0 139 

10.559 
10.679 
10.800 
10.922 
1 1.04 1 
11.167 
11.291 
11.415 

11.534 
1 1.666 
l 1 793 
l 1.920 
12.048 
12.176 
12.305 
12.435 

12.566 
12.697 
12.829 
12.962 
13.095 
13.229 
13.304 
13.499 

13.635 
13.772 
13.909 

14.047 
14.186 
14.325 
14.465 
14.G06 



Dia. in 

ft. in. 

4 

4 

4 

4 

4 

l 

4 

4 



Cir. in 
ft. in. 



4 


13 




4', 


13 


8% 


41, 


13 


8% 


4% 


13 


9% 


.» 


13 


10% 


5% 


13 


11% 


5% 


1 1 







14 


0% 


6 


14 


IB* 


<'-', 


14 




6% 


14 


3% 




14 


4 


7 


14 


'■| 


7% 


14 


5% 



'•'1 

8 

8% 

8% 

9 

9% 
9% 
9% 

10 
10% 

111'-.. 

10% 

1 1 

11% 
11% 
11% 



0% 

111.. 

0% 

1 

1% 
1% 
1% 



2% 
3 

3% 
3% 

3% 

4 

4i, 

4% 

4% 

5 

5% 

5% 

5% 



15 
15 
15 
15 
15 
15 
15 
15 



16 
16 
16 
16 
16 
16 
16 
16 



6 
7% 



14 7% 

i i m 

14 9% 

14 10% 
11 11 
II 11% 

15 i»'s 
15 1% 



2% 
2% 

:: : , 
1% 
5% 
6% 

6% 

7- ; , 



15 9% 

15 I" 

15 10% 

15 11% 

16 0% 

16 l', 
16 1% 



i»; 
i<; 

i<; io% 
16 11% 



2% 

:;i, 

5% 

6% 
7% 
8% 

9 

9% 



17 
17 
17 
17 



0% 

0% 

1% 

2% 



Area in 
sq. inch. 
2123.72 
2144.19 

2164.75 
2185.42 
2206.18 
2227.05 
2248.01 
2269.06 

2290.22 
231 1.48 
2332.83 
2354.28 

2::7:>.s:; 
2397.48 
2410.22 
2441.07 

2463.01 
2485.05 
2507.19 
2529.42 
2551.76 
2574.19 
2596.72 
2619.35 

2642.08 
2664.91 
2687.83 
2710.85 
2733.97 
2757.19 
2780.51 
2803.92 

2827 14 
2851.05 
2874.76 
2898.56 
2922.47 
2946.47 
2970.57 
2994.77 

3019.07 

.••.in::. 4 7 
3067.96 
3092.56 

31 17.25 
3142.04 
3166.92 
3191.91 

3216.99 

3242.17 

32 07. 40 
3292.83 
3318.31 
3343.88 

3369.56 

3395.33 



Area in 
sy. ft. 
14.748 
14.890 
15.033 
15.176 
15.320 
15.465 
15.611 
15.757 

15.904 
16.051 

1 0.200 

16.349 
16.498 
16.649 
16.800 
16.951 

17.104 
17.256 

17,111 
17.565 
17.720 
17.876 
18.033 
18.189 

18.347 
18.506 
18.665 
18.825 
18.965 
19.1 17 
19.309 
19.471 

19.635 

10. 7! IS 
19.963 
20.128 
20.294 
211.401 
20 629 
20.797 

20.965 
21.135 
21.305 
21.476 
21.647 
21.819 
21.992 
22.100 

22.333 
22.515 

22.021 
22.S00 
23.043 
23.221 
23.330 
23.578 



102 



Tables, Rules and Recipes. 



Dia. in 


Cir 


. in 


Area in 


Area in 


Dia. in 


Cir 


. in 


Area in 


Area in 


ft. 


in. 


ft. 


iu. 


sq. Inch. 


sq. ft. 


it. 


in. 


ft. 


in. 


sq. inch. 


sq. ft. 


5 


6 


17 


3% 


3421.20 


23.758 


1; 


4 


19 


10% 


4536.47 


31.50.i 


5 


G& 


17 


4% 


3447.16 


23.938 


G 


4V 4 


19 


11% 


4566.36 


31.710 


5 


6% 


17 


4% 


::47:;.j:; 


24.119 


6 


4% 


20 


0V 4 


4596.35 


31.910 


5 


6% 


17 


5% 


3499.39 


24.301 


6 


4% 


1*0 


1% 


1626.44 


3J.114 


5 


7 


17 


6% 


3525.26 


24.483 


6 


5 


20 


l T s 


4656.63 


32.337 


5 


7% 


17 


7% 


3552.01 


24.666 


t; 


5% 


20 


2% 


4686.92 


32.548 


5 


7% 


17 


8 


3578.47 


24.850 


6 


5% 


20 


3% 


1717.30 


32.759 


5 


7% 


17 


s% 


3605.03 


25.034 


6 




20 


"I 1 ! 


4747.70 


32.970 


5 


s 


17 


9% 


3631.68 


25.220 


<; 


6 


20 


."» 


4778.37 


33.183 


5 


8% 


17 


10% 


3658.44 


25. 4<ir> 


6 


6% 


20 


5% 


1809.05 


33.396 


5 


8% 


17 


11% 


3685.29 


2 5 . 5 '• ' 2 


6 


6% 


20 


6% 


4839.83 


33.619 


5 


8% 


17 


ll T / 8 


3712.24 


25.779 


6 


6% 


20 


7% 


4870.70 


33.824 


5 


9 


is 


0% 


3739.28 


25.964 


<; 


7 


20 


8% 


4901.68 


34.039 


5 


9% 


IN 


1% 


3766.43 


26.155 


G 


i^ 


20 




1932.75 


34.255 


5 


!•'., 


IS 


2% 


3793.67 


26.344 


6 


t ' ■. 


20 


'•'•, 


4963.92 


34. 17 1 


T> 


9% 


IS 


3% 


3821.02 


26.534 


c. 


7% 


•Jo 


10% 


1995.19 


34.688 


5 


10 


18 


3% 


3848 If. 


26.725 


6 


s 


20 


11% 


5026.26 


34.906 


5 


10Vi 


is 




3875.99 


26.916 


6 


- 


•Jl 


0% 


5058.02 


:\:,.\\::< 


5 


10% 


18 


5% 


3903.63 


27.108 


(i 


M.. 


21 


0% 


5089.58 


35.34 1 


5 


10% 


18 


6% 


3931.36 


27.301 


6 


&% 


21 


lg 


5121.24 


35.564 


5 


11 


18 


7 


3959. n\ 


27.494 


6 


9 


•Jl 




5153.00 


35 784 


r> 


11', 


18 




3987.13 


27.688 


6 


9% 


21 


3% 


5184.86 


36.006 


5 


11% 


18 


4015.16 


27.883 


6 


9% 


21 


1 


5216.82 


36.227 


5 


11% 


18 




4043.28 


28.078 


6 


9% 


Jl 


l', 


5248.87 


36.450 


6 





18 


10% 


1071.51 


28.274 


6 


10 


21 




5281.02 


:w;.<;7 i 


6 


0% 


18 


10% 


4099.83 


28 47 1 


6 


10% 


21 




5313.27 


36 897 


6 


0% 


is 


11% 


4128.25 


28.663 


6 


10% 


21 


7% 


5345 82 


37.122 


6 


0% 


19 


0% 


4156.77 


28.866 


1; 


10% 


21 


7% 


5378.07 


37.347 


6 


1 


19 


l'i 


H85.39 


29 Ofi I 


6 


11 


21 




5410.62 


37.573 


♦; 


1% 


19 


2% 


4214.11 


29.264 


6 


11% 


21 


9% 


54 13.26 


37.700 


6 


1% 


19 


2% 


1242 92 


29.466 


6 


11% 


21 


10% 


5476.00 


38.027 


G 


3% 


lit 


3% 


4271.83 


29.665 


6 


1 1"'. 


21 


11 


5508.84 


38.256 


6 


• > 


10 


4% 


4300 85 


29.867 














6 

t; 


21 i 


10 
19 


5% 
6 


4329.95 
4359.16 


30.069 
30.271 














6 


2% 


19 


6% 


1388. »7 


30.475 














R 


3 


19 


7% 


\ H7.87 


30.619 














6 
6 


3% 


10 

19 


9% 


4447. :i7 
447C. 07 


30.884 
31.090 














6 


3% 


19 


9% 


450G.G7 


31.296 















Tables, Rules and Recipes. 



103 



Dia. in 

ft. in. 

7 

7 1 

7 2 



7 6 

7 7 

7 8 

7 9 

7 10 

7 11 




1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 


1 
2 
:•. 
I 
5 

6 

7 

8 

9 

10 



9 11 



10 

10 

111 
10 

1() 
10 
10 

10 

10 
10 



10 10 
10 11 



Circum. in 


ft. 


in. 


21 


11% 


22 


3 


22 


6% 


.,•> 


'•"» 


23 


0% 


23 


2% 


23 


6% 


23 


11 


2 1 


U6 


2 1 


4'. 


24 


7 '4 


24 


10% 


25 


L% 


25 


1% 


25 


7% 


25 


1 1 


26 


2% 


26 


•»'. 


26 




26 


llVs 


27 




•J 7 


5% 


27 


g 


:> 


0% 


28 


3% 


28 


6% 


28 


9% 


29 


0% 


29 


::■'•, 


29 


7 


29 


10% 


30 


1% 


30 


t% 


30 


7% 


30 


11% 


31 


1% 


31 


5 


31 


8% 


::i 


11% 


32 




32 


5% 


32 


8% 


32 


11% 


33 


2% 


33 


6% 


33 


9% 


34 


0% 


34 


3y 2 



Area in feet. 
38.4846 

39.4060 

40.3388 
41.2825 
42.23U7 
4:;. 2022 
44.17^7 
45.1656 
46.1638 
47.1730 
48.1926 
49.2236 

50.2656 
51.6178 
52.3816 
53.4562 
54.5412 
55.6377 
56.7451 
57.8628 
58 9920 
60.1321 
61.2826 
62.4 1 15 

63.6174 
64.8006 
65.9951 
67.2007 
68.4166 
69.6440 
70.8823 
72.1309 
73.3910 
74.6620 
75.9433 

77.2362 

78.5400 
79.8540 
81.1795 
82.5190 

83.8627 
85.2211 
86.5903 
87.9697 

80.366S 
90.7627 
92.1749 
93.5986 



Dia. in 

ft. in. 



Circum. in 
ft 



I 1 

I I 
1 1 
11 
11 
11 
11 
11 
11 
11 



12 
12 

12 
12 
12 
12 
12 
12 
12 
12 



1 3 
13 
13 
13 
13 
1 3 
13 
13 
13 
13 
13 
1:1 



11 10 

11 11 



12 in 
12 11 



8 



1(1 
11 



1 1 

14 

1 I 

14 

14 

14 

1 1 

11 

14 

14 9 

14 10 

14 11 



34 
34 
35 
35 
35 



in. 

6% 
9% 
0% 
4V 8 
7% 



3.") 10% 

36 1% 

30 4% 

36 7% 

36 10% 

37 2% 
37 5% 

37 8% 
.",7 11% 

38 2% 



38 
38 
39 
39 
39 
39 
40 
40 
40 



5% 


3% 

6% 
91. , 
0% 
3% 
6% 



40 10 

41 1% 
41 4% 

41 7M; 
4 1 10% 

42 1% 
42 4% 
4 2 8 

42 11% 

43 214 
43 5% 
43 8% 

43 11% 

44 2% 



H 
41 



6 

9% 



45 01/, 
45 3% 



45 
45 

46 
46 
46 



6% 
9% 

CVS 

4 

7Vs 



46 11% 



Area in feet. 

95.0334 

96.4783 

97.9347 

99.4021 

ltto.8797 

102.3689 

103. 8601 

105.3794 

106.9013 

108.4342 

109.9772 

111.5319 

113.0976 
1 1 1.6732 
116.2007 
117.8590 
119.4674 
121.0876 
122.7187 
124.350:' 
126.0127 
127.6765 
129.3504 
131.0369 

132.7326 
134.4391 
136.1574 
137.8867 
139.6260 
1 11.3771 
143.1301 
144.0111 
1 16.6949 
148.4896 
150.2043 
152.1109 

153.9484 
155.7758 
157.6250 
159.4852 
161.3553 
163.2373 
165.1303 
167.0331 
168.9479 
170.8735 
172.8091 
174.7565 



io4 



Tables, Rules and Recipes. 



I)ia 


. in 


Circum. in 




Dia 


in 


«'ircum. in 




ft. 


in. 


ft. 


in. 


Area in feet. 


ft. 


in. 


ft. 


in. 


Area in feet. 


L5 





47 


1', 


176.7150 


17 


<> 




1% 


226.9806 


15 


1 


47 


I ft 


178.6832 


IT 


1 


53 


B 


229.2105 


15 


2 


47 


7 ; , 


180.6624 


IT 


'J, 


53 


11% 


231.4625 


15 


:: 


47 


10% 


182.6545 


1 7 


3 


54 




233.7055 


10 


i 






184.6555 


IT 


4 


54 




235.9682 


L5 


5 


4^ 




186.6684 


1 7 


."> 


54 


M.. 


238.2430 


15 


6 


18 




188 6923 


IT 


•; 


54 


11% 


240.5287 


L5 


7 


18 


1 1 •_ 


190.7260 


1 T 


T 


.... 


- T . 


242.8241 


15 


8 


19 


2% 


192.7716 


IT 


8 


55 


6 


245.1316 


15 


g 


49 


■<■■, 


194.8282 


1 T 


9 


:. :. 


'••'* 


247.4500 


15 


io 


19 


8% 


196.8946 


IT 


10 






249.7781 


i:> 


n 


50 


«' 


198.9730 


IT 


1 1 


56 


••••'-■ 


252.1184 


16 





50 


3% 


201.0624 


is 





56 




254.4696 


16 


i 


50 


<••'. 


203.1615 


L8 


1 


56 




256.8303 


16 


2 


50 




205.2726 


is 


•• 


5 1 


0% 


259.2033 


16 


3 


51 


0% 


207.3946 


18 


3 


.">T 


1 


261.5872 


16 


1 


51 




209.526 1 


18 


l 


57 


7% 


263.9807 


16 


- 


r.1 


»;i., 


211.6703 


is 


5 


57 


1" , 


266.3864 


16 


»; 


:.1 


10 " 


213.8251 


is 


6 


58 




268.8031 


it; 


7 


52 


1% 


215.9896 


18 


T 






271.2293 


16 


8 


52 


»', 


218.1662 


is 


s 






273.6678 


11; 


9 


52 




220.3537 


is 


9 


58 


1095 


276.1171 


16 


10 


52 


111'.. 


222 5510 


18 


10 


59 


2 


278.5761 


IS 


li 


53 




224 7603 


is 


11 






281.0472 



WEIGHT PER FOOT OF LEAD PIPE. 



Inside 


AAA 


A A 




A 




B 




C 




> 


E 


diam- 


B 


•ook- 




•]\. 














I 


X. 


Foun- 


eter. 


Ivn. 


strong. 


Si i 


• Mm. 


Me< 


liuni. 


I. 


ght. 


light. 


tain. 


Ins. 


Lb. 


« >. . 


Lb. 




Lb 


Oz. 


Lb. 




LI 


. Oz. 


Lb. 





LI.. Oz. 




1 


L2 


1 


8 


1 


1 


1 


ii 


ii 


L2 


ii 


in 


1 7 


7-16 














1 


ii 


ii 


13 








', 


3 


6 


2 


ii 


1 


12 


1 


1 


1 





n 


12 


ii 


% 


3 


- 


• > 


12 


• > 


s 


2 


(1 


1 


8 


1 





(1 12 


% 


1 


12 


:; 


B 


3 


II 


• > 


t 


1 


12 


1 


\ 


1 <» 


1 


6 





4 


12 


1 





;; 


1 


• > 


s 


2 





1 8 


1% 


<; 


12 


.i 


L2 


t 


12 


3 


12 


:; 


II 


'2 


8 


2 n 


1 ' . 


8 


8 


7 


8 


6 


s 


.~i 


ii 


I 


4 


:; 


s 


3 o 


l& 


10 


ii 


s 


8 


7 


II 


r. 





r» 


ii 


4 








o 


11 


12 


9 


U 


8 





7 





u 





1 


12 





e i - — >-. » > - - ' a 
-r. ^> = ~ —i — : i -J 

T ^r uS ITS LS LS Lrt O 



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OS 3 t— CO iS i- o r I 
O '.O rH ".O — < \0 T i i - 
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lQ t— Of< is t~ O '-O 
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ri I- CO x5c0 0»-*0 



krf t-i »ci t>i eo oi-^5 50 

COCOCOCOOCDcOCOt-» 



S^s&ft^c&S £;£&£&§*£ ^^as^jft&s 5 ^sft&jft&s- 



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3 2 10 2£ °9 fc- S t»« 

as r: ,- — 



% = - - 7 . - - X 

— • 30 - 1 -' ' ' ■ ' SO 55 



.•1 / : - 1 x ■ - 



'■ 1 EC '- = ~ ~J -/ — 
- = £ -. 

1 - ■ ! 8 ' . — ' x . . ■ 1 

■ :' ■ " '■ — 

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-- — •' — 55 ' I - 



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— 1 - 1 - '^ 31 ■* M CO 

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1 .d-V::'-'.^',-' .= _ / -T: / J , .: / ::'*,/ .E-'-T::^^^ 



to IM 






: — n 1- 

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"■ ■ ". - 1 - x 



..,-: 1 :■ r. ~ -^ -r 

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•_•:, — so >q r-; ■* i- 
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.= J-"::' J'.-'::".' E-^: 7 -' 7 ^- 7 .= -' -":/ - ' ■■' -"-' .= ^ ^ »' ~ ''^^ '"V 



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= JS- 



i-hnt;z .:-m- 

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:::; — — — -r -r -r iSiriiSiSin 



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= _' _V- 



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<3 • ^ h ,-: c i c i z i .-•-:':-' —' — 1 -',-' •-' , ^ i - A >5 OS O j-h t-j c -| co t>J J£5 l ^ ^ !^ S 5§ 

a* . " T d 

— . r-l : 1 CO ■* C1 

r,:: of Tin: 1ai-.lt:: To find the capacity of any cylindrical measure, 
from 1 inch diameter to 30 indies, take the inside diameter of the meas- 
ure in inches, and multiply the area in the table which corresponds tc 
the diameter by the depth in Inches, and divide the products if gill* 
are required, by 7.2135 ; if pints, by 28.875 ; if quarts, by 57.75 ; and if gal- 
lons, by 231. If bushels are required (say in a tierce or ban'el, after tn- 
mean diameter is obtained), multiply as above, and divide the product 
by 2150.42 : the quotient is trie number of bushels. Calling the diameteis 
feet the areas are feet.— then, if a ship's water tank, steam boiler etc., 
is 5y s . or anv number of feet and parts of feet in diameter nnd the 
area in the table which corresponds in inches, multiply it by the lengtn 
in feet, and multiply this result bv the number of gallons in a cubic 
foot (7.4805), and the product is the answer in gallons. In any case 
where there are more figures in the divisor than in the dividend, add 
ciphers. 



106 Tables, Rules and Recipes. 

CAPACITY OF CANS ONE IXCH DEEP. 



USE OF THE TABLE. 

Required the contents of a vessel, diameter 6 7-10 Inches, depth 10 
inches. 

By the table o vessel l Inch deep and 6 MO Inches diameter contains 
.15 (hundredths) gallon, then 15 X 10 = L50, or l gallon and 2 quarts. 

Required the contents of a can, diameter L9 8-10 inches, depth 30 
Inches 

By the table a vessel l Inch deep and 198-10 Inches diameter con- 
tains l gallon and .33 (hundredths), then 1.33 x 30 = 39.90, or nearly 40 
gallons. 

Required the depth of a can whose diameter is 12 2-10 Inches, to 
contain 16 gallons. 

By the table a vessel 1 inch deep and 12 2-10 inches diameter contains 
.50 (hundredths) gallon, then 16 ■*- .50 = 32 inches, the depth required. 



DIam 


. 




















eter. 






Vio 


Vio 


Vio 




Vio 


V.o 


Vio 


Vio 


3 


.03 


.03 


.03 


.03 


.03 


Ji4 






.04 


.05 


4 ■ 


.06 




.05 






.06 


.07 


.oT 


.67 


.08 


5 


.08 


.MS 


.08 






.10 


.10 


.11 


.11 


.11 


6 


.12 


.12 


.12 


.13 


.13 


.14 


.14 


.15 


.16 


.16 


7 


,16 


.17 


.17 


.18 


.is 


.19 


.19 


.20 




.21 


8 


.21 


.22 


.... 


.23 


.23 


.24 




.26 


.26 


.26 


9 


.27 


.28 






.30 


.30 


.31 


.31 


.32 


.33 


10 


.34 


.34 


.36 


.36 




.37 






.39 


.10 


11 


.n 


.41 




.43 


.44 


.41 


.46 


.46 


.47 


is 


12 


.is 


.49 


.50 


.:,1 


.52 


.53 




.64 


.55 




13 


.57 


.58 


.59 


.60 




.61 




.63 


.64 


.65 


14 


.66 


.67 


.68 


.69 


.70 


.71 


.72 




.74 


.75 


15 


.76 


.77 


.78 




.80 


.si 


.82 


.83 


.84 




16 


.ST 


.88 


.89 


.90 


.91 


.92 




.94 


.95 


.97 


17 


.98 


.99 


1.005 


1.017 


1.028 


L040 


1.061 


L063 


1.076 


1.086 


18 


1.10] 


1.113 


l . 1 26 




1.150 


L162 


l.lTo 


1.187 


1.200 


1.211 


19 


1 ' ,-, 7 


L240 


1.253 


1.266 


1.279 


1.292 




L317 


1.330 


L343 


20 


L360 


1.373 


1.386 


L400 


1.414 


MI'S 


1.441 


1 . 166 


1 ITS 


1 . 182 


21 


L499 


1.513 


1.527 


1.542 


1.556 


1.570 




1.600 


1.612 


1 630 


'"2 


1.646 


L660 


1.675 


1.696 


1.706 


1.720 


1.735 


1.760 


l 770 


L780 


23 


L.798 


1.814 




L845 


1.861 


is;,; 


L892 


L908 


1.923 


1.940 


24 


1.958 


1.974 


1.991 


2.007 


2.023 


2.040 




2.072 




2.105 


25 


2.125 


2.142 


2.159 


2.176 


2.193 


2.12H 


2.227 


'.'.211 


2.261 


2.280 


26 


2.298 


2.316 


2.333 


2.361 


2.369 




2.404 




2.446 


2.460 


27 


2.478 


2. 196 


2.515 




2.552 


2.570 




2.607 




2.643 


28 


2 665 


2.684 


2.703 


2 722 


2.741 


2.764 




2.800 


2.820 




29 


2.859 


2.879 


2 898 


2.918 






2.977 


2.997 


3.017 


3.036 


30 


3.060 


3.080 


3.100 


3.121 


3.141 


3.162 


3.182 


3.202 


3.223 


3.246 


::i 


3.267 


3.288 


3.309 


3.330 


3.351 




3.393 


3.414 


3.436 


3.457 


32 


3.481 


3.503 


3.524 


3.543 


3.568 


3.590 


3.612 


3.633 


3.655 


3.589 


33 


3.702 


3.725 


3.747 


3.773 




3.814 




3.860 


3.882 


3.904 


34 


3.930 


3.953 


3.976 


1.003 


4.022 


4.046 


4.070 


i.o«.i2 


1.115 


4 llo 


35 


4.165 


4.188 


4.212 


4.236 


1.260 


1.284 


4.307 


4.331 


1.366 


4.380 


36 


4.406 


4.430 


4.465 


4.483 


4.503 


4.528 


1.553 


L577 


4.602 


4.626 


37 


4.654 


4.679 


4.704 


1.730 


1.755 


4.780 


4.805 


4.834 


4.855 


4.880 


38 


4.909 


4.935 


4.961 


4.987 


5.012 


5.038 


6.064 


5.090 


5.120 


5.142 


39 


5.171 


5.197 


5.224 


5.250 




5.304 


5.330 


5.357 


5.383 


5.410 


40 


5.440 


5.467 


6.491 




5.548 


5.576 


5.603 


5.630 


5.657 


5.684 



Tables, Rules and Recipes. 107 

RULES FOR CALCULATING CIRCUM- 
FERENCES. 

1st. Multiply the given diameter by 22, and divide the 
product by 7 ; or 2d, divide 22 by 7 and multiply the di- 
ameter by the quotient ; or 3d, multiply the diameter by 
3.1416; or 4th, multiply the diameter by 3 and add 1 inch 
for every 7 of the diameter, or about y% inch for every 1. 
For example: If the given diameter be 15 inches, by the 
first rule the circumference would be 47 1-7 inches ; by the 
second, 47 1-7 inches ; by the third, 47.1240 inches; by the 
fourth, 47J/8 inches; by the table. XJ X A inches. It will be 
seen that the result is not just the same by the several 
rules, yet either is near enough for general use and prac- 
tice. 

WEIGHT OF WATER. 

1 cubic inch is equal to .0361 7 pound. 

12 cubic inches is equal to .434 pound. 

1 cubic fool is equal to <i*J.."> pounds. 

1 cubic fool is equal to 7.50 I T .S. gallons. 

1.8 cubic feel isequalto 112.00 pounds. 

3f>.84 cubic feet is equal to 2240.00 pounds. 

1 cylindrical inch is equal to .02842 pound. 

12 cylindrical inches isequalto .341 pound. 

cylindrical foot isequalto 49.10 pounds. 

1 cylindrical foot isequalto <;.0() U.S. gallon' 

2.282 cylindrical feet isequalto 112.00 pounds. 

4r>.<;4 cylindrical feet isequal to 2240.00 pounds. 

13.43 United States gallons. ..isequalto 111'. <><> pounds. 

268.8 United States gallons ... is equal to 2240.00 pounds. 

Center of pressure is at two-thirds depth from surface. 

TO FIND NUMBER OF BARRELS IN 
CISTERNS. 

The following table shows the number of barrels (31^ 
gallons) contained in cisterns of various diameters, from 
5 to 30 feet, and of depths ranging from 5 to 20 feet 



io8 



Tables, Rules and Recipes. 



To use the table, find the required depth in the side 
column, and then follow along the line to the column 
which has the required diameter at the top. Thus, with 
a cistern 6 feet deep and 16 feet in diameter, we find 6 
in the second line, and then follow along until column 16 
is reached, when we find that the contents is 286.5 barrels. 

NUMBER OF BARRELS (31^ GALLONS) IN CISTERNS AND 

TANKS. 



Diameter in feet. 



Depth in 


















feet. 5 


6 


7 


8 


9 


10 


11 


12 


13 


5 


23.3 


33.6 


4:,. 7 


59.7 


75.5 


93.2 


112.8 


134.3 


157.6 


6 


28.0 


40.3 


54.8 


71.7 


90.6 


111.9 


135.4 


161.1 


189.1 


7 


32.7 


47.0 


04.0 


83.6 


105.7 


130.6 


158.0 


188.0 


220.6 


8 


37.3 


53.7 


73.1 


95.5 


120.9 


149.2 


180.5 


214.8 


252.1 


9 


42.0 


60.4 


82.2 


107.4 


136.0 


107.9 


203.1 


241.7 


283.7 


10 


46.7 


07.1 


91.4 


119.4 


151.1 


186.5 


225.7 


268.6 


315.2 


11 


51.3 


73.9 


100.5 


13L3 


166.2 


2i»5.1 


248.2 


295.4 


346.7 


12 


56.0 


80.6 


109.7 


143.2 


181.3 


223.8 


270.8 


322.3 


378.2 


13 


Gii.7 






L55.2 


196.1 


242.4 


293.4 


349.1 


4U9.7 


14 


65.3 


94.0 


127.9 


167.1 


211.5 


261.1 


315.9 


376.0 


441.3 


15 


70.0 


L00.7 


137.1 


179.0 


226.6 


289.8 


338.5 


402.8 


472.8 


16 


74.7 


107.4 


146.2 


191.0 


241.7 


298.4 


361.1 


429.7 


504.3 


17 


79.3 


114.1 


155.4 


202.9 


250.S 


317.0 


383.6 


456.6 


535.8 


18 


84.0 


120.9 


164.5 


214.8 


272.0 


335.7 


406.2 


483.4 


567.3 


19 


88.7 


127.6 


17::. 


226.8 


287.0 


354.3 


428.8 


510.3 


598.0 


20 


93.3 


134.3 


182.8 


238.7 


302.1 


373.0 


451.3 


537.1 


630.4 










Diamet 


er in feet. 








Depth in 


















feet 


;. 14 


15 


16 


17 


18 


19 


20 


21 


22 


5 


182.8 


209.8 


238.7 


269.5 


302.1 


336.6 


373.0 


411.2 


451.3 


6 


219.3 


251.8 


286 5 


323.4 


362.0 


404.0 


447.6 


493.5 


541.6 


7 


255.9 


293.7 


J!34 2 


377.3 


423.0 


471.3 


522.2 


575.7 


631.9 


3 


292.4 


335.7 


382.0 


431.2 


483.4 


538.f 


596.8 


658.0 


722.1 


9 


329.0 


377.7 


429.7 


485.1 


543.S 


605.9 


671.4 


740.2 


812.4 


10 


365.5 


419.6 


477.4 


539.0 


604.3 


673.3 


746.0 


822.5 


902.7 


11 


402.1 


461.6 




592.9 


667.7 


740.6 


820.6 


904.7 


992.9 


12 


438.6 


503.5 


572.9 


616.8 


725.1 


807.9 


895.2 


987.0 


1083.2 




475.2 


545.5 


620.7 


700.7 


785.5 


875.2 


969.8 


1069.2 


1173.5 


14 


511.8 


587.5 


668.2 


754.6 


846.6 


942.6 


1044.4 


1151.5 


1263.7 


15 


548.3 


029.4 


716.2 


808.5 


906.0 


1009.9 


1119.0 


1233.7 


1354.0 


16 


584.9 


071.4 


77::. 9 


862.4 


966.8 


1077.2 


1193.6 


1315.9 


1444.3 


17 


621.4 


713.4 


811.6 


916.3 


1027.2 


1144.6 


1268.2 


1398.2 


1534.5 


IS 


658.0 


755.3 


859.4 


97(1.2 


1087.7 


1211.9 


1342.8 


1480.4 


1624.8 


19 


694.5 


797.3 


907.1 


1024.1 


1148.1 


1279.2 


1417.4 


1562.7 


1715.1 


20 


731.1 


839.3 


954.9 


1078.0 


1208.5 


1346.5 


1492.0 


1644.9 


1805.3 



Tables, Rules and Recipes. 



109 



Diameter in feet. 



Depth in 



feet 


. 23 


24 


25 


26 


27 


28 


29 


30 


5 


493.3 


537.1 


582.8 


630.4 


679.8 


731.1 


784.2 




6 




644.5 


699.4 


756.5 


M5.X 


877.3 


941.1 


1007.1 


7 


690.6 


752.0 


815.9 


882.5, 


951.7 


1023.5 


1097.9 


1175.0 


8 


789.3 


859.4 


932.5 


1008.6 


1087.7 


1169.7 


1254. X 


1342.8 


9 


887.9 


966.8 


1049.1 


1134.7 


L223.6 


1316.0 


1411.6 


1510.7 


10 


986.6 


1074.2 


1165.6 


1260.8 


1359.6 


1162.2 


156S.2 


1678.5 


11 


Ins:,.:: 


1181.7 


1282.2 


1386.8 


1495.6 


1608.7 


1723.0 


1846.4 


12 


1183.9 


1289.1 


1398.7 


1512.9 


1631.5 


1754.fi 


1882.2 


2014.2 


i.; 


1282.6 


1396.5 


1515.3 


1639.0 


1767.5 


1900.8 


2039.0 


2182.0 


11 


1381.2 


1503.9 


1631.9 


1765.1 


1903.4 


2047.1 


2195.9 


2343.9 


15 


1479.9 


Mil. 4 


1748.4 


1891.1 


2039.4 


2193.3 


2352.7 


2517.8 


it; 


L578.5 




1S65.0 


20172 


2175.4 


2339.5 


2509.6 


2685.6 


17 


1677.2 


1826.2 


1981.6 


2143.3 


2S11.3 


2485.7 


2666. 1 


2853.5 


18 


1775.9 


1933.6 


2098.1 


2269.4 


2447.3 


2631.9 


2823.3 


3021.3 


19 


1874.5 


2041.1 


2214.7 


2395.4 




277S.1 


29S0.1 


3189.2 


20 


1973.2 


2148.5 


2321.2 


2521.5 


2719.2 


2924.4 


3137.0 


3357.0 



For tanks that are tapering the diameter may be measured four- 
tenths from large end. 

TABLE SHOW IXC THE PRESSURE 01- WATER PER SQUARE 
INCH, DUE TO DIFFERENT HEADS, FROM 1 TO 250 FEET. 



Head. Pressure in lbs. Head. Pressure in lbs. 



Head. Pressure in lbs. 



1 


.4335 


J9 


8.237 


37 


16.04 


2 


.8670 


20 


8X70 


38 


16.47 


3 


1.300 


21 


9.104 


39 


16.91 


4 


1.734 


22 


9.537 


40 


17.34 


5 


2.167 


23 


9.971 


50 


21.67 


6 


2.601 


24 


10.40 


100 


43.35 


7 


3.035 


25 


10.84 


110 


47.68 


8 


3.408 


26 


11.27 


120 


52.02 


9 


3.902 


27 


11.70 


130 


56.36 


10 


4.335 


28 


12.14 


140 


60.69 


11 


4.768 


29 


12.57 


150 


65.03 


12 


5.202 


30 


13.00 


160 


69.36 


13 


5.636 


31 


13.44 


170 


73.70 


14 


6.069 


32 


13.87 


180 


78.03 


15 


C.503 


33 


14.S1 


190 


82.36 


16 


6.936 


34 


14.74 


200 


86.70 


17 


7.370 


35 


15.17 


225 


97.41 


18 


7.803 


36 


15.60 


250 


108.37 



MEASURES OF CAPACITY AND WEIGHT. 
Measures of Weight. — Avoirdupois. — 16 drams 
equal 1 ounce; 16 ounces 1 pound; 112 pounds 1 hundred- 
weight ; 20 hundredweights 1 ton. Troy. — 24 grains 1 
pennyweight; 20 pennyweights 1 ounce; 12 ounces 1 
pound. Apothecaries'. — 20 grains equal 1 scruple ; 3 
scruples i dram; 8 drams i ounce; 12 ounces 1 pound. 



no Tables, Rules and Recipes. 

Measures of Capacity (Dry). — 2150.42 cubic inches 
equal 1 United States (or Winchester) bushel; the di- 
mensions of which are iSy 2 inches diameter inside, 19^2 
inches outside and 8 inches deep ; 2747.70 cubic inches 
equal 1 heaped bushel, the cone of which must not be less 
than 6 inches high. 

Measures of Capacity (Liquids). — 231 cubic inches 
equal 1 United States standard gallon ; 2JJ.2J<\ cubic 
inches equal 1 Imperial (British) gallon; 31^ United 
States gallons equal 1 barrel ; 42 gallons equal 1 tierce ; 
63 gallons equal 1 hogshead ; 84 gallons equal 1 puncheon ; 
126 gallons equal 1 pipe; 252 gallons equal 1 tun. 

French Measures of Frequent Reference, Com- 
pared with U. S. Measures. — Meter, 3.28 feet ; Deci- 
meter (1-10 meter), 3.94 inches; Centimeter, .4 inch; 
Millimeter, .04 inch; Hectoliter, 26.42 gallons; Liter, 2. n 
pints ; Kilogram, 2.2 pounds. 

Weights of Various Substances. — Pounds Avoir- 
dupois. — 1 cubic foot of bricks weighs 124 pounds; 1 do. 
of sand or loose earth, 95 ; 1 do. of cork, 15 ; 1 do. of gran- 
ite, 170; 1 do. of cast iron, 450; 1 do. of wrought iron, 
485; 1 do. of steel, 490; 1 do. of copper, 555; 1 do. lead, 
709; 1 do. brass, 520; t do. tin, 459; 1 do. white pine, 30; 
1 do. oak, 48 ; 1 do. sea water, 64.08 ; 1 do. fresh. 62.35 ; 
1 do. air, 0765. 



Tables, Rules and Recipes. 



in 



CAPACITY OF CYLINDERS IN IMPERIAL GALLONS 

This table gives the number of Imperial gallons (277.274 inches) in cylindrical 
vessels from 1 to 72 inches in depth and from 4 to 72 inches in diameter. 

Diameter in Inches. 



Depth. 



10 



lin. 


.0453 


.0708 


.102 


.1388 


.1814 


. 2295 


.2833 


2 


.0906 


.1416 


.204 


. 2776 


.3628 


.4590 


.5666 


3 


.1359 


.2124 


.306 


.4104 


.5442 


.6885 


.8499 


4 


.1812 


.2832 


.408 


.5552 


.7256 


.9180 


1.1332 


5 


.2265 


. 3540 


.510 


.6940 


.9070 


1.1475 


1.4165 


6 


.2718 


.4248 


.612 


.8328 


1 . 0884 


1.3770 


1 . 6998 


7 


.3171 


.4956 


.714 


.9716 


1.1698 


1 . 6065 


1.9831 


8 


.3624 


.5664 


.816 


1.1104 


1.4512 


1 . 8360 


2 . 2664 


9 


.4077 


.6372 


.918 


1.2492 


1 . 6326 


2.0655 


2 . 5497 


10 


.4530 


.7080 


1.020 


1 . 3880 


1.8140 


2 . 2950 


2 . 8330 


11 


.4983 


.7788 


1.122 


1 . 5268 


1 . 9954 


2.5245 


3.1163 


12 


.5436 


.8496 


1.224 


1 . 6656 


2.1768 


2.7540 


3 . 3996 


13 


. 5889 


. 9204 


1.326 


1 8044 


2 . 3582 


2.9835 


3 . 6829 


14 


.6342 


.9912 


1.428 


1.9432 


2 . 3396 


3.2130 


3 . 9662 


15 


.6795 


1.0620 


1 . 530 


2 . 0820 


2.7210 


3.4425 


4.2495 


16 


.7248 


1.1328 


1.632 


2 . 2208 


2.9024 


3.6720 


4.5328 


17 


.7701 


1 . 2036 


1 . 734 


2 . 3596 


3.0838 


3.9015 


4.8161 


18 


.8154 


1.2744 


1 .836 


2 . 4984 


3.2652 


4.1310 


5 . 0994 


19 


.8607 


1.3452 


1.938 


2.6372 


3.4466 


4 . 3605 


5.3827 


20 


.9060 


1.4160 


2.040 


2.7760 


3 . 6280 


4 . 5900 


5.6660 


21 


.9513 


1 . 4868 


2.142 


2.9148 


3 . 5094 


4.8195 


5.9493 


22 


.9966 


1 . 5576 


2.244 


3.0536 


3 . 9908 


5 . 0490 


6.2326 


23 


1.0419 


1 . 6284 


2.346 


3.1924 


4.1722 


5.2785 


6.5159 


24 


1.0872 


1 . 6992 


2.448 


3.3312 


4 . 3536 


5.5080 


6.7992 


25 


1.1325 


1 . 7700 


2.550 


3 . 4700 


4 . 5350 


5.7375 


7 . 0825 


26 


1.1778 


1 . 8408 


2.652 


3 . 6088 


4.7164 


5.9670 


7.3658 


27 


1.2231 


i '.tut; 


2.754 


3.7476 


4 . 8978 


6.1965 


7.6491 


28 


1 . 2684 


1 . 9824 


2 . 856 


3 . 8864 


4 . 6792 


6.4260 


7.9324 


29 


1.3137 


2.0532 


2.95S 


4 . 0252 


5 . 2606 


6.6555 


8 . 3057 


30 


1 . 3590 


2.1240 


3.060 


4.1640 


5.4420 


6 . 8850 


8.4990 


31 


1.4043 


2.1948 


3.162 


4 . 3028 


5.6234 


7.1145 


8.7823 


32 


1.4496 


2.2656 


3 . 264 


4.4416 


5 . 8048 


7 . 3440 


9 . 0656 


33 


1.4949 


2 . 3364 


3 . 366 


4 . 5804 


5.9862 


7 . 5735 


9 . 3489 


34 


1 . 5402 


2.4072 


3.468 


4.7192 


6.1676 


7 . 8030 


9.6322 


35 


1 . 5855 


2.4780 


3.570 


4 . 8580 


6 . 3490 


8.0325 


9.9155 


36 


1 . 6308 


2 . 5488 


3.672 


4 . 9968 


6.5304 


8.2620 


10.1988 


40 


1.8120 


2 . 8320 


4.080 


5.5520 


7 . 2560 


9 . 1800 


11.3320 


44 


1.9932 


3.1152 


4.489 


6.1072 


7.9816 


10.0980 


12.4652 


48 


2.1744 


3 . 3984 


4.896 


6.6624 


8.7072 


11.0160 


13 . 5984 


54 


2.4462 


3.8232 


5.508 


7.4952 


9.7956 


12.3930 


15.2982 


60 


2.7180 


4 . 2480 


6.120 


8.3280 


10 . 8840 


13.7700 


16.9980 


72 


3.2616 


5.0976 


7.344 


9.9936 


13.0608 


16.5240 


20.3976 



112 



Tables, Rules and Recipes. 



CAPACITY OF CYLINDERS IN IMPERIAL GALLONS— Continued 

Diameter in Inches. 



Depth. 



11 



12 



13 



14 



15 



16 



lin. 


.3428 


.4080 


.4788 


.5553 


.6375 


.7253 


2 


.6856 


.8160 


.9576 


1.1106 


1 . 2750 


1.4506 


3 


1 . 0284 


1.2240 


1.4364 


1 . 6659 


2.0125 


2.1759 


4 


1.3712 


1 . 6320 


1.9152 


2.2212 


2 . 5500 


2.9012 


5 


1.7140 


2 . 0400 


2 . 3940 


2.7765 


3.1875 


3.6265 


6 


2 . 0568 


2.4480 


2 . 8728 


3.3318 


3 . 8250 


4.3518 


7 


2.3996 


2.8560 


3.3516 


3.8871 


4.3625 


5.0771 


8 


2 . 7424 


3.2640 


3 . 8304 


4.4424 


5.1000 


5.8024 


9 


3 . 0852 


3.6720 


4.3092 


4.9977 


5.7375 


6.5277 


10 


3.4280 


4.0800 


4.7880 


5.5530 


6.3750 


7.2530 


11 


3.7708 


4.4880 


5.2668 


6.1083 


7.0125 


7.9783 


12 


4.1136 


4 . 8960 


5.7456 


6.6636 


7.6500 


8.7036 


13 


4.4564 


5 . 3040 


6.2244 


7.2189 


8.2875 


9.4289 


14 


4.7992 


5.7120 


6.7032 


7.7742 


8.7250 


10.1542 


15 


5.1420 


6.1200 


7.1820 


8.3295 


9.5625 


10.8795 


16 


5.4848 


6.5280 


7 . 6608 


8.8848 


10.2000 


11.6048 


17 


5.8276 


6.9360 


8.1396 


9.4401 


10.8375 


12.3301 


18 


6.1704 


7.3440 


8.6184 


9.9954 


11.4750 


13.0554 


19 


6.5132 


7.7520 


9.0972 


10.5507 


12.1125 


13.7807 


20 


6.8560 


8.1600 


9.5760 


11.1060 


12.7500 


14 . 5060 


21 


7.1988 


8.5680 


10.0548 


11.6613 


13.0875 


15.2313 


22 


7.5416 


8.9760 


10.5336 


12.2166 


14.0250 


15.9566 


23 


7 . 8844 


9 . 3840 


11.0124 


12.7719 


14.6625 


16.6819 


24 


8.2272 


9.7920 


11.4912 


13.3272 


15.3000 


17.4072 


25 


8.5700 


10.2000 


11.9700 


13.8825 


15.9375 


18.1325 


26 


8.9128 


10.6080 


12.4488 


14.4378 


16.5750 


18.8578 


27 


9.2556 


11.0160 


12.9276 


14.9931 


17.2125 


19.5831 


28 


9 . 5984 


11.4240 


13.4064 


15.5484 


17.4500 


20.3084 


29 


9.9412 


11.8320 


13.8852 


16.1037 


18.4875 


21.0337 


30 


10.2840 


12.2400 


14.3640 


16.6590 


20.1250 


21.7590 


31 


10.6268 


12.6480 


14 . 8428 


17.2143 


19.7625 


22.4843 


32 


10.9696 


13.0560 


15.3216 


17.7696 


20.4000 


23.2096 


33 


11.3124 


13.4640 


15.8004 


18.3249 


21.0375 


23.9349 


34 


11.6552 


13.8720 


16.2792 


18.8802 


21.6750 


24 . 6602 


35 


11.9980 


14.2800 


16.7580 


19.4355 


21.8125 


25.3855 


36 


12.3408 


14.6880 


17.2368 


19.9908 


22 . 9500 


26.1108 


40 


13.7120 


16.3200 


19.1520 


22.2120 


25.5000 


29.0120 


44 


15.0832 


17.9520 


21.0672 


24.4332 


28.0500 


31.9132 


48 


16.4544 


19.5840 


22 . 9824 


26.6544 


30.6000 


34.8144 


54 


18.5112 


22 . 0320 


25.8552 


29.9862 


34.4250 


39.1702 


60 


20.5680 


24.4800 


28.7280 


33.3180 


38.2500 


43.5180 


72 


24.6816 


29.3760 


34.4736 


39.9816 


45.9000 


52.2216 



Tables, Rules and Recipes. 



"3 



CAPACITY OF CYLINDERS IN IMPERIAL GALLONS— Continued 

Diameter in Inches. 



Depth. 



17 



18 



19 



20 



21 



24 



lin. 


.8188 


.9180 


1.0228 


1.1333 


1.2495 


1 . 632 


2 


1.6376 


1 . 8360 


2.0456 


2.2666 


2 . 4990 


3.264 


3 


2.4564 


2 . 7540 


3.0684 


3 . 3999 


3 . 7485 


4.986 


4 


3.2752 


3.6720 


4.0912 


4 . 5332 


4.9980 


6.528 


5 


4.0940 


4 . 5900 


5.1140 


5.6665 


6.2475 


8.160 


6 


4.9128 


5.5080 


6.1368 


6.7998 


7.4970 


9.792 


7 


5.7316 


6 . 4260 


7.1596 


7.9331 


8.7465 


11.424 


8 


6 . 5504 


7.3440 


8.1824 


9.0664 


9.9960 


13.056 


9 


7.3692 


8.2620 


9.2052 


10.1997 


11.2455 


14 . 688 


10 


8.1880 


9 . 1800 


10.2280 


11.3330 


12.4950 


16.320 


11 


9.0068 


10.0980 


11.2518 


12.4663 


13.7445 


17.952 


12 


9 . 8256 


11.0160 


12.2736 


13.5996 


14.9940 


19 . 584 


13 


10.6444 


11.9340 


13.2964 


14 . 7329 


16.2435 


21.216 


14 


11.4632 


12.8520 


14.3192 


15.8662 


17.4930 


22.848 


15 


12.2820 


13.7700 


15.3420 


16.9995 


18.7425 


24.480 


16 


13.1008 


14 . 6880 


16.3648 


18.1328 


19.9920 


26.112 


17 


13.9196 


15.6060 


17.3876 


19.2661 


21.2415 


27.744 


18 


14 . 7384 


16.5240 


18.4104 


20.3994 


22.4910 


29.376 


19 


15.5572 


17.4420 


19.4332 


21.5327 


23 . 7405 


31.008 


20 


16.3760 


18.3600 


20.4560 


22.6660 


24 . 9900 


32.640 


21 


17.1948 


19 . 2780 


21.4788 


23 . 7993 


26 . 2395 


34 . 272 


22 


18.0136 


20.1960 


22 . 5036 


24.9326 


27 . 4890 


35 . 904 


23 


18.8324 


21.1140 


23.5244 


26.0659 


28.7385 


37.536 


24 


19.6512 


22 . 0320 


24 . 5472 


27.1992 


29 . 9880 


39.168 


25 


20.4700 


22.9500 


25.5700 


28.3325 


31.2375 


40.800 


26 


21.2888 


23 . 8680 


26 . 5928 


29.4658 


32.4870 


42.432 


27 


22.1076 


24.7860 


27.6156 


30.5991 


33.7365 


44 . 064 


28 


22.9264 


25.7040 


28.6384 


31.7324 


34.9860 


45.696 


29 


23.7452 


26.6220 


29.6612 


32 . 8657 


36.2355 


47.328 


30 


24.5640 


27 . 5400 


30.6840 


33.9990 


37.4S50 


48.960 


31 


25.3828 


28.4580 


31.7068 


35.1323 


38.7345 


50.592 


32 


26.2016 


29 . 3760 


32.7296 


36.2656 


39.9840 


52 . 224 


33 


27 . 0204 


30.2940 


33.7554 


37.3989 


41.2335 


53.856 


34 


27.8392 


31.2120 


34 . 7752 


38.5322 


42.4830 


55.488 


35 


28.6580 


32 . 1300 


35.7980 


39 . 6655 


43.7325 


57.120 


36 


29.4768 


33 . 0480 


36 . 8208 


40.7988 


44.9820 


58.752 


40 


32.7520 


36.7200 


40.9120 


45.3320 


49.9800 


65.280 


44 


36.0272 


40.3920 


45.0072 


49 . 8652 


54.9780 


71.808 


48 


39 . 3024 


44 . 0640 


45.0944 


54 . 6384 


59.9760 


78.336 


54 


44.2152 


49 . 5720 


55.2312 


61.1982 


67.4730 


88.128 


60 


49 . 1280 


55.0800 


61.3680 


67.9980 


74.9700 


97.920 


72 


58.9536 


66.0960 


73.6416 


81.5976 


89.9640 


117.504 



ii4 



Tables, Rules and Recipes. 



CAPACITY OF CYLINDERS IN IMPERIAL GALLONS— Continued 

Diameter in Inches. 



Depth. 



30 



36 



40 



48 



DO 



72 



lin. 


2.55 


3.672 


4.5333 


6.528 


10.2 


14 . 688 


2 


5.10 


7.344 


9 . 0666 


13.056 


20.4 


29.376 


3 


7.65 


11.016 


13.5999 


19 . 584 


30.6 


44 . 064 


4 


10.20 


14.688 


18.1332 


26.112 


40.8 


58.752 


5 


12.75 


18.360 


22.6665 


32 . 640 


51.0 


73 . 440 


6 


15.30 


22.032 


27.1998 


39.168 


61.2 


88.128 


7 


17.85 


25.704 


31.7331 


45.696 


71.4 


102.816 


8 


20.40 


29.376 


36.2664 


52 . 224 


81.6 


117.504 


9 


22.95 


33 . 048 


40.7997 


58.752 


91.8 


132.192 


10 


25.50 


36.720 


45.3330 


65.280 


102.0 


146.880 


11 


28.05 


40.392 


49.8663 


71.808 


112.2 


161.568 


12 


30.60 


44 . 064 


54 . 3996 


78.336 


122.4 


176.256 


13 


33.15 


47.736 


58.9329 


84 . 864 


132.6 


190.944 


14 


35.70 


51.408 


63 . 4662 


91.382 


142.8 


205 . 632 


15 


38.25 


55.080 


67.9995 


97.920 


153.0 


220.320 


16 


40.80 


58.752 


72 . 5328 


104.448 


163.2 


235 . 008 


17 


43.35 


62.424 


77.0661 


110.976 


173.4 


249 . 696 


18 


45.90 


66.096 


81.5994 


117.504 


183.6 


264 . 384 


19 


48.45 


69 . 768 


86.1327 


124.032 


193.8 


279.072 


20 


51.00 


73.440 


90.6660 


130.560 


204.0 


293.760 


21 


53.55 


77.112 


95.1999 


137.088 


214.2 


308.448 


22 


56.10 


80.784 


99.7326 


143.616 


224.4 


323.136 


23 


58.65 


84.456 


104 . 2659 


150.144 


234.6 


337.824 


24 


61.20 


88.128 


108.7992 


156.672 


244 . 8 


352.512 


25 


63.75 


91.800 


113.3325 


163.200 


255.0 


367 . 200 


26 


66.30 


95.472 


117.8658 


169.728 


265.2 


381.888 


27 


68.85 


99 . 144 


122.3991 


176.256 


275.4 


396 . 576 


28 


71.40 


102.816 


126.9324 


182 . 784 


285.6 


411.264 


29 


73.95 


106.488 


131.4657 


189.312 


295.8 


425.952 


30 


76.50 


110.160 


135.9990 


195.840 


306.0 


440.640 


31 


79.05 


113.832 


140.5326 


202.368 


316.2 


455.328 


32 


81.60 


117.504 


145.0656 


208.896 


326.4 


470.016 


33 


84.15 


121.176 


149.5989 


215.424 


336.6 


484 . 704 


34 


86*. 70 


124.848 


154.1322 


221.952 


346.8 


499 . 392 


35 


89.25 


128.520 


158.6655 


228 . 480 


357.0 


514 . 080 


36 


91.80 


132.192 


163.1988 


235.008 


367.2 


528.768 


40 


102 . 00 


146.880 


181.3320 


261.120 


408.0 


587.520 


44 


112.20 


161.568 


199.4652 


287 . 232 


448.8 


646.272 


48 


122.40 


176.256 


217.5984 


313.344 


489.6 


705.024 


54 


137.70 


198.288 


244 . 2982 


352.512 


550.0 


793.152 


60 


153 . 00 


220.320 


271.9980 


391.680 


612.0 


881.280 


72 


183.60 


264 . 384 


326.3976 


470.016 


734.4 


1057 . 536 



Tables, Rules and Recipes. 115 

TABLE OF EFFECTS UPON BODIES BY HEAT. 

Degrees F. 

Cast iron thoroughly melts at 2,228 

Gold melts at 1.9J3 

Silver melts at M*J 

Copper melts at 1070 

Brass melts at • vm 

Zinc melts at ■ u -' 



Lead melts at 



tns 



Bismuth melts at ^6 

Tin melts at 444 

Tin and lead, equal parts, melt at 4is 

Tin 2 parts, bismuth 5 and lead 3. melt at u» 



PRACTICAL RECEIPTS. 

SOLDERS. 

SOLDER FOR GOLD. 

Gold, 6 pennyweights ; silver, 1 pennyweight ; copper, 
2 pennyweights. 

SOLDER FOR SILVER, FOR THE USE OF JEWELERS. 

Fine silver, 19 pennyweights; copper, 1 pennyweight; 
sheet brass, 10 pennyweights. 

WHITE SOLDER FOR SILVER. 

Silver, 1 ounce ; tin, 1 ounce. 

WHITE SOLDER FOR RAISED BRITANNIA WARE. 

Tin, 100 pounds; copper, 3 ounces; to make it free, 
add lead, 3 ounces. 

BEST SOFT SOLDER FOR CAST BRITANNIA WARE. 

Tin, 8 pounds ; lead, 5 pounds. 

YELLOW SOLDER FOB BRASS OR COPPER. 

Copper, 1 pound ; zinc, 1 pouna. 



n6 Tables, Rules and Recipes. 

YELLOW SOLDER FOR BRASS OR COPPER. 

(Stronger than the last.) Copper, $2 pounds; zinc, 
29 pounds ; tin, 1 pound. 

SOLDER FOR COPPER. 

Copper, 10 pounds ; zinc, 9 pounds. 

BLACK SOLDER. 

Copper, 2 pounds ; zinc, 3 pounds ; tin, 2 ounces. 

BLACK SOLDER. 

Sheet brass, 20 pounds ; tin, 6 pounds ; zinc, 1 pound. 

SILVER SOLDER FOR PLATED METAL. 

Fine silver, 1 ounce; brass, 10 pennyweights. 

plumbers' solder. 
Lead, 2 ; tin, 1 part. 

tinmen's solder. 
Lead, 1 ; tin, 1 part. 

PEWTERERS' SOLDER. 

Tin, 2; lead, 1 part. 

HARD SOLDER. 

Copper, 2 ; zinc, 1 part. 

SOLDER FOR STEEL JOINTS. 

Silver, 19 pennyweights; copper, 1 pennyweight; 
brass, 2 pennyweights. Melt under a coat of charcoal 
dust. 

SOFT GOLD SOLDER 

Is composed of 4 parts gold, 1 of silver and 1 of copper. 
It can be made softer by adding brass, but the solder be- 
comes more liable to oxidize. 



Tables, Rules and Recipes. 117 

CEMENT FOR MENDING EARTHEN AND GLASS WARE. 

I. Heat the article to be mended a little above boiling 
water heat, then apply a thin coating of gum shellac on 
both surfaces of the broken vessel, and when cold it will 
be as strong as it was originally. 2. Dissolve gum shellac 
in alcohol, apply the solution and bind the parts firmly 
together until the cement is perfectly dry. 

CEMENT FOR STONE WARE. 

Another cement in which an analogous substance, the 
curd of milk, is employed, is made by boiling slices of 
skim milk cheese into a gluey consistence in a great quan- 
tity of water, and then incorporating it with quicklime 
on a slab with a muller, or in a marble mortar. When 
this compound is applied warm to broken edges of stone 
ware, it unites them very firmly after it is cold. 

IROX RUST CEMENT 

Is made from 50 to 100 parts of iron borings, pounded and 
sifted, mixed with 1 part of sal ammoniac, and when it is 
to be applied, moistened with as much water as will give 
it a pasty consistency. Another composition of the same 
kind is made by mixing 4 parts of fine borings or filings of 
iron, 2 parts of potters' clay and 1 part of pounded pot- 
sherds, and making them into a paste with salt and water. 

CEMENT FOR IRON TUBES, BOILERS, ETC. 

Finely powdered iron, 66 parts; sal ammoniac, 1 part; 
water, a sufficient quantity to form a paste. 

CEMENT FOR IVORY, MOTHER OF PEARL, ETC. 

Dissolve 1 part of isinglass and 2 of white glue in 30 
of water, strain and evaporate to 6 parts. Add 1-30 part 



it8 Tables, Rules and Recipes. 

of gum mastic, dissolve in l / 2 part of alcohol and I part of 
white zinc. When required for use warm and shake up. 

CEMENT FOR HOLES IN CASTINGS. 

The best cement for this purpose is made by mixing 
I part of sulphur in powder, 2 parts of sal ammoniac and 
80 parts of clean powdered iron turnings. Sufficient 
water must be added to make it into a thick paste, which 
should be pressed into the holes or seams which are to be 
filled up. The ingredients composing this cement should 
be kept separate and not mixed until required for use. It 
is to be applied cold, and the casting should not be used for 
two or three days afterward. 

CEMENT FOR COPPERSMITHS AND ENGINEERS. 

Boiled linseed oil and red lead mixed together into a 
putty is often used by coppersmiths and engineers to se- 
cure joints. The washers of leather or cloth are smeared 
with this mixture in a pasty state. 

A CHEAP CEMENT. 

Melted brimstone, either alone or mixed with rosin 
and brick dust, forms a tolerably good and very cheap 
cement. 

plumbers' cement 

Consists of black rosin, 1 part ; brick dust, 2 parts ; well 
incorporated by a melting heat. 

cement for bottle corks. 

The bituminous or black cement for bottle corks con- 
sists of pitch hardened by the addition of rosin and brick 
dust. 



Tables, Rules and Recipes. no 

CHINA CEMENT. 

Take the curd of milk, dried and powdered, 10 ounces ; 
quicklime, 1 ounce ; camphor, 2 drams. Mix and keep in 
closely stopped bottles. When used, a portion is to be 
mixed with a little water into a paste, to be applied quickly 

CEMENT FOR LEATHER. 

A mixture of India rubber and shellac varnish makes 
a very adhesive leather cement. A strong- solution of 
common isinglass, with a little diluted alcohol added to 
it, makes an excellent cement for leather. 

MARBLE CEMENT. 

Take plaster of paris and soak it in a saturated solu- 
tion of alum, then bake the two in an oven, the same as 
gypsum is baked to make it plaster of paris ; after which 
they are ground to powder. It is then used as wanted, 
being mixed up with water like plaster and applied. It 
sets into a very hard composition capable of taking a very 
high polish. It may be mixed with various coloring min- 
erals to produce a cement of any color capable of imitating 
marble: 

CEMENT FOR MARBLE WORKERS AND COPPERSMITHS. 

White of an <tgg alone, or mixed with finely sifted 
quicklime, will answer for uniting objects which are not 
exposed to moisture. The latter combination is very 
strong and is much employed for joining pieces of spar 
and marble ornaments. A similar composition is used by 
coppersmiths to secure the edges and rivets of boilers, only 
bullock's blood is the albuminous matter used instead of 
white of Qgg. 



120 Tables, Rules and Recipes. 

TRANSPARENT CEMENT FOR GLASS. 

Dissolve I part of india rubber in 64 of chloroform, 
then add gum mastic in powder 14 to 24 parts, and digest 
for two days with frequent shaking. Apply with camel's 
hair brush. 

CEMENT TO MEND IRON POTS AND PANS. 

Take 2 parts of sulphur, and 1 part, by weight, of fine 
black lead; put the sulphur in an old iron pan, holding it 
over the fire until it begins to melt, then add the lead, stir 
well until all is mixed and melted, then pour out on an 
iron plate or smooth stone. When cool, break into small 
pieces. A sufficient quantity of this compound being 
placed upon the crack of the iron pot to be mended, can 
be soldered by a hot iron in the same way a tinsmith 
solders his sheets. If there is a small hole in the pot, drive 
a copper rivet in it and then solder over it with this ce- 
ment. 

CEMENT TO RENDER CISTERNS AND (ASKS WATER TIGHT. 

An excellent cement for resisting moisture is made by 
incorporating thoroughly 8 parts of melted glue, of the 
consistence used by carpenters, with 4 parts of linseed oil, 
boiled into varnish with litharge. This cement hardens 
in about 48 hours and renders the joints of wooden cis- 
terns and casks air and water tight. A compound of 
glue with one-quarter its weight of Venice turpentine, 
made as above, serves to cement glass, metal and wood to 
one another. Fresh made cheese curd and old skim milk 
cheese, boiled in water to a slimy consistency, dissolved in 
a solution of bicarbonate of potash are said to form a 
good cement for glass and porcelain. The gluten of 



Tables, Rules and Recipes. 121 

wheat, well prepared, is also a good cement. White of 
eggs with flour and water, well mixed, and smeared over 
linen cloth, forms a ready lute for steam joints in small 
apparatus. 

A GOOD CEMENT. 

Shellac, dissolved in alcohol or in a solution of borax, 
forms a pretty good cement. 

CEMENT FOR REPAIRING FRACTURED BODIES OF ALL KINDS. 

White lead ground upon a slab with linseed oil varnish 
and kept out of contact of air affords a cement capable 
of repairing fractured bodies of all kinds. It requires a 
few weeks to harden. When stone and iron are to be ce- 
mented together, a compound of equal parts of sulphur 
with pitch answers very well. 

CEMENT FOR CRACKS IN WOOD. 

Make a paste of slaked lime 1 part, rye meal 2 parts, 
with a sufficient quantity of linseed oil. Or dissolve 1 
part of glue in 16 parts of water, when almost cool stir in 
sawdust and prepared chalk a sufficient quantity. Or 
oil varnish thickened with a mixture of equal parts of 
white lead, red lead, litharge and chalk. 

CEMENT FOR JOINING METALS AND WOOD. 

Melt rosin and stir in calcined plaster until reduced to 
a paste, to which add boiled oil a sufficient quantity to 
bring it to the consistence of honey ; apply warm. Or, 
melt rosin 180 parts and stir in burnt umber 30, calcined 
plaster 15 and boiled oil 8 parts. 

GAS FITTERS' CEMENT. 

Mix together resin 4^ parts, wax 1 part, and Venetian 
red 3 parts. 



122 Tables, Rules and Recipes. 

IMPERVIOUS CEMENT FOR APPARATUS, CORKS, ETC. 

Zinc white rubbed up with copal varnish to fill up the 
indentures ; when dry, to be covered with the same mass 
somewhat thinner, and lastly with copal varnish alone. 

CEMENT FOR FASTENING BRASS TO GLASS VESSELS. 

Melt rosin 150 parts, wax 30, and add burnt ocher 30 
and calcined plaster 2 parts. Apply warm. 

CEMENT FOR FASTENING BLADES, FILES, ETC. 

Shellac 2 parts, prepared chalk 1, powdered and mixed. 
The opening for the blade is filled with this powder, the 
lower end of the iron heated and pressed in. 

HYDRAULIC CEMENT PAINT. 

If hydraulic cement be mixed with oil, it forms a first 
rate anti-combustible and excellent water proof paint for 
roofs of buildings, outhouses, walls, &c. 

TO STOP A LEAKY ROOF. 

Twenty-five pounds yellow ocher, 1 pound litharge, 
6 pounds black lead, 1 pound fine salt ; boil well in oil. 
Soak strips of cloth in the above and paste over the seams. 
Good where solder is not practicable. 

FLUX FOR SOLDERING TIN ROOF. 

One part rosin and 2 parts binnacle oil mixed hot and 
used the same as rosin alone ; or, cut with alcohol 1 pint 
as much rosin as possible and put on with a swab. Either 
good when the wind blows. Or saponified or red oil used 
with a swab along the seams. Solder flows more freely 
than with rosin alone. 



Tables, Rules and Recipes. 123 

SOLDERING FLUID OR FLUX. 

Prussiate of potash, borax and copperas, each 1 dram ; 
sal ammoniac l / 2 ounce, muriatic acid 3^ ounces, well 
mixed, then add as much zinc as it will dissolve. Add 
1 pint or more water according to strength required. 

ANOTHER. 

Sal ammoniac and borax, each 1 dram ; chloride of 
zinc 1 ounce, water 1 pint. It will not eat copper or tar- 
nish tin. Use less water and it will be stronger. 

PREPARATION AXD APPLICATION OF ALUMINUM SOLDERS. 

Tin, 95 to 99: Bismuth, 5 to 8. 

This composition, which is an ordinary soft solder, is 
adapted for soldering aluminum by means of the common 
soldering iron. 

Zinc, 80 Copper, 8 Aluminum, 12 

Zinc, 85 Copper, 6 Aluminum, 5 

Zinc, 90 Copper, 4 Aluminum, 6 

In preparing aluminum solders the alloy of copper 
and aluminum is always made first and the zinc added. 
The zinc used should contain no iron as it will affect the 
fusibility and durability of the solder. In preparing the 
solder, first melt all the copper, then add the aluminum 
gradually. The two metals are of a very different density 
and the mixture should be stirred with an iron rod to 
unite them as far as possible. There is no solder which 
operates with aluminum in the same way as ordinary 
solder works with copper, tin, etc. This is due to the 
fact that aluminum will not alloy readily with solders 
with temperatures so low as the other metals require. 



124 Tables, Rules and Recipes. 

Then, it is also covered with a thin coating of aluminum 
oxide, which is very refractory. All the surface to which 
it is intended that the solder shall adhere must first be 
tinned. This is accomplished by heating the metal to a 
temperature above the fusion point of the solder used 
and then rubbing the surface with a stick of the solder ; 
thus rubbing the oxide off the surface with the solder 
itself and covering the exposed points with melted solder 
all in the same motion. After the edges to be united are 
thus tinned they may be sweated together with pure block 
tin with the aid either of a soldering iron or blast lamp. 
It is well to bear in mind that solder will not flow into an 
aluminum joint even when tinned, by capillary action, as 
it does into copper or tin joints, and it is therefore neces- 
sary to place on the surface of the metal all of the 
material necessary to sweat them together before the 
edges are brought into contact. 



Practical Sheet Metal Work 

AND DEMONSTRATED PATTERNS 



A carefully selected series of articles on shop and outside 
practice from the Metal Worker with additional new matter to 
make each volume cover its field completely. 

This set of books has been published to meet the demand for 
the articles on pattern drafting and cutting as well as the 
many excellent methods for forming up and handling material 
which have been printed in the Metal Worker. All of this 
material was arranged according to the phase of metal work to 
which it related and it was then carefully edited by Mr. J. 
Henry Teschmacher, an expert, and only the best methods were 
retained. Much new material was added by the editor to make 
each separate volume complete, and we feel that the work 
forms a veritable encyclopedia on all phases of sheet metal 
work. 



I. Leaders & Leader Heads, 113 
pages, 150 figures. 

II. Gutters & Roof Outlets, 116 
pages, 194 figures. 

III. Roofing, 138 pages, 207 figures. 

IV. Ridging & Corrugated Iron 

Work, 132 pages, 239 figures. 

V. Cornice Patterns, 119 pages, 
1 95 figures. 

VI. Circular Cornice Work, 126 
pages, 194 figures. 



VII. Practical Cornice Work, 139 

pages, 237 figures. 
VIII. Skylights, 122 pages, 260 
figures. 
IX, Furnace & Tin Shop Work, 
145 pages, 239 figures. 
X. Piping & Heavy Metal Work, 
144 pages, 259 figures. 

XI. Automobile & Sheet Metal 
Boats, 137 pages, 193 
figures. 
XII. Special Problems, 154 pages, 
150 figures. 



1575 pages. 8£ X 11 inches. 2517 Illustrations. Cloth. 
Single Volumes, $1.50. The Set, $15.00. 



SENT PREPAID BY 

DAVID WILLIAMS COMPANY 

239 West 39th Street, New York 



THE EVERREADY PIPE AND 
ELBOW CHART 

(Designed by M. W. Pehl) 

A New Short Gut Method of Laying Out Elbows 
Made of celluloid with one large central and two smaller (rotating discs 
A KEY TO RAPID AND ACCURATE WORKMANSHIP 



With this little chart half the time usually requii 

lay out elbow or p | the chart gives tin- Length <>t throat 

for any size pipe from 3 to 62 inches and for any number of pieces with laps 

■ r shows 
md area of all sizes of pipe, from s to 6a inches inclu- 

Full instru irding the use of the Chart are given in a 1 

which is supplied with it. : numerous diagrams makes 

imple and • Many valuable tables giving the 

of various materials arc also include 1, together with much pi 
■1 heating an 1 ventilating work. 
A lew of the principal articles are: 

Circumference including laps for all sizes of pipes from 3" to 62". 

Areas of all sizes of pipes from .V to §2". 

Length of throat of 4, 5, 6 piece elbows all radius from .V to 62". 

Deductions from s nail ends from No. 26 to gauge steel. 

Tapering joints of all sizes. 

Length of throat for 8, 10, 12, 15, 16, 18, 20, 24 piece elbow. 

Elbows of less than 90 decrees. 

Mitre lines for 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 24, piece elbows. 

Laying out elbows. 

Weight of galvanized pipe per lineal foot No. 26, 2 1, 22, 20 gauge. 

Weight of galvanized elbows of an\ radius. 

Weight of galvanized ducts from !"X )" to 1 1 ' 5 " X 1 1 ' 5" in three 

gauges. 
Weight of black and galvanized steel per square foot. 

The Booklet is bound in durable linen with a pocket in the inside front 
cover for the Chart. It is small enough to go in the hip-pocket. It was 
made for you — send for it and profit. 



Price Complete, 75 cents Postpaid. 



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239 West 39th Street, ----- New York 



THE NEW 

Metal Worker Pattern Book 

A TREATISE ON PATTERN CUTTING 

AS APPLIED TO ALL BRANCHES 

OF SHEET METAL WORK 

By GEO. W. KITTREDGE 

[| covers the subject so thoroughly and accurately that it is 
called "The Bible of the Sheet Metal Worker." Every detail 
of the work is taken up systematically from the selection of the 
instruments, through linear drawing, geometrical drawing and 
the principles of pattern cutting to the problems in laying 
out which range from the simple elbow work to the very diffi- 
cult problems where triangulation is thoroughly explained. 

Features which make the work exceptionally popular are the 
chapters on drawing and geometrical problems, which explain 
these usually difficult and discouraging subjects so clearly that 
no one can fail to understand them. ... As a book for home 
study it has no equal. 

The Principal Contents 

Terms and Definitions — 15 Pages— Explaining the various terms employed 
by Draftsmen, Architects and Mechanics. Drawing Instruments and Mate- 
rials— 13 Pages — Describing the tools and materials used by Draftsmen. 
Linear Drawing— 6 Pages— Explaining the principles of geometrical drawings 
as applied to the wants of the pattern cutter. Geometrical Problems — 
35 Pages — Containing 85 problems of most frequent occurrence and sup- 
plementing the previous chapter. Principles of Pattern Cutting — 25 
Pages — Explaining the theory of pattern cutting as applied to all classes 
of work. Pattern Problems (3 Sections) — 325 Pages — 1. Miter Cutting. 
2. Flaring Work. 3. Triangulation. A collection of practical examples 
of work daily encountered by Cornice Workers and Tinners and of frequent 
occurrence with Builders. 



438 Pages. 10X13 inches. 744 Illustrations. Cloth. 
Price $5.00 Delivered. 



DAVID WILLIAMS COMPANY 

239 West 39th Street, - New York 



TO HANG UP IN THE SHOP 



THE METAL WORKER SHOP CARDS 

Presenting a Series of Useful Tables Convenient for Reference 



Every shop needs a set of these cards for they give the information 
you want the minute it is needed. They arc printed on heavy manila 
of best quality 10JX14 inches in size and are eyeletted for hanging 
right handy to the work. 

If you have ever figured the time lost in looking up the size sheet required 
for a tank or cylinder of givi or in getting the area of a circle. 

nothing more need be said in favor of the cards. 

No. i -The Quantity of Tin Required for Roofs (Flat and Standing 

Seam) With Rules for Calculating Roof 
No. J -The Diameters. Areas and Circumferences of Circles. 

Advancing by eighths, from 1 inch to 54] inches. With full Direc- 
tions for Use; also Tables of Conversion of Inches and Eighths into 
Decimals of a Foot, and n of Vulgar Fractions into 

Decimals; also Rules relating to the Circle. 
No. S —Capacity of Cylinders in United States Gallons; with Direc- 
tions for" Use and a schedule of Decimal Equivalents Of the 
Fractional Parts of a Gallon. 

PRICE 25 CENTS EACH. PER SET, *U) < / \ 7 V 



MENSURATION FOR SHEET METAL WORKERS 

AS APPLIED IN WORKING ORDINARY PROBLEMS IN SHOP PRACTICE 

With 71 Figures 
By WILLIAM NBUBBCKBR 

This new book contains an easily applied explanation of the 

principles of mensuration (the art of measurements), showing 
its practical application in solving the great number of prob- 
lems that arise in finding the areas, dimensions, or capaci- 
ties of the different sizes and shapes ol sheet metal products 
turned out from the shop. 

A very handy aid in computing the measurements of 
material by correct methods, and invaluable to the mechanic, 
shop foreman, and apprentice. 

51 Pages. Cloth Covers. 50 Cents, Postpaid 



DAVID WILLIAMS COMPANY 

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METAL WORKER 



You want the news of your trade in a clear 
and interesting form with a lot of particulars 
about new tools, machinery and apparatus, so 
written that you would rather read it than your 
daily paper. 

You desire to be posted regarding the latest 
ideas on the design and installation of heating 
and plumbing systems, to know about the best 
ideas in pattern cutting and you desire to know 
the solution of the problems of the cornice maker, 
the plumber and the stove-man. 

A knowledge of what the other man is doing 
is a mighty good business asset, and the advice 
of the best brains and talent of trained experts 
in your line is at your command. 

For nearly forty years METAL WORKER 
has been the recognized authority and technical 
adviser of the sheet metal, plumbing and heating, 
steam-fitting, ventilating, tool and machinery 
trade. 

METAL WORKER comes from the press 
every week at a cost to you of only $2.00 a year. 

Any issue you miss may contain just the 
particular article that will be of greatest value 
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M ETAL WORKER 

139 WEST :59TH STREET, NEW YORK CITY 



IR 2 1912 



